Kleene stephen c (25 Ergebnisse)
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American scientist : Autumn 1969, Vol 57, No.3 [Panta Rhei, and so flow our nerves; Death from lightning & the possibility of living again; Palynology & environmental history during the Quaternary Period; The new logic; Formal characterics of pictograms]
Taylor, Hugh ; Sigma Xi. [Paul A Weiss, Helen B Taussig, Margaret B Davis, Stephen C Kleene, Paul A Kolers, Selman A Waksman, Leonard Berkowitz, Lynn White
Verlag: [New Haven, Conneticut : Society of the Sigma Xi], 1969. 1969
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Soft cover. Zustand: Very Good. pgs 317-388 (71 pp.), 175A-300A (125 pp.) ; paper wrappers ; Contents: New and Views -- Panta Rhei, and so flow our nerves / Paul A Weiss -- Death from lightning and the possibility of living again / Helen B Taussig -- Palynology and environmental history during the Quaternary Period / Margaret B…Davis -- The new logic / Stephen C Kleene -- Some formal characterics of pictograms / Paul A Kolers -- Microbiology as a field of science and application / Selman A Waksman -- Simple views of aggression, and essay review / Leonard Berkowitz -- Letters to the editor: Carlton W Berenda, R B Partridge, R G Schipf, Richard L Newman, Robert Stephanos, A G Smith, Gustav Winkler, F W Went, J C Hsu ; wear to edges ; some pages uncut ; VG. Book.
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413 pp. In-8 - br., qqs. rouss. sur la couv.
Sprache: Englisch
Verlag: New York and Oxford Oxford University Press and Clarendon Press 1986 1986
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FIRST EDITION 8vo. dark blue cloth hardback, gilt, in unclipped dust jacket. 474pp., Indexed. A clean copy with no markings or inscriptions.A couploe of small closed tears to dust jacket edges, else a VERY GOOD COPY in VERY GOOD DUST JACKET. (Shelf 7/200) ISBN: 0195039645 PLEASE NOTE: Buyer is responsible for any additional duti…es, taxes, or fees required by recipient's country.** Pictures available upon request.** Visit our homepage for our shop opening hours. Over 20,000 books in stock - come and browse. PayPal, credit and most debit cards welcome. Books posted worldwide. For any queries please contact us direct.
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Zustand: Sehr gut. Zustand: Sehr gut | Seiten: 424 | Sprache: Englisch | Produktart: Bücher | This second volume of a comprehensive edition of Gödel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of hi…s previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks.
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Zustand: New. This second volume of a comprehensive edition of logician Godel's works collects together all his publications from 1938 to 1974. Together with Volume I, it makes available for the first time in a single source all of his previously published work. Editor(s): Feferman, Solomon; Dawson, John W., Jr.; Kleene, Stephen… C.; Moore, Gregory H.; Solovay, Robert M.; Heijenoort, Jean van. Num Pages: 432 pages, 5 halftones. BIC Classification: HPL; PBCD. Category: (P) Professional & Vocational. Dimension: 234 x 158 x 23. Weight in Grams: 640. . 1990. Revised ed. paperback. . . . . Books ship from the US and Ireland.
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Hardcover. Zustand: Brand New. 11th repr. 1996 edition. 550 pages. 9.25x6.25x1.25 inches. In Stock.
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Zustand: gut. Collected Works. Vol. 2: Publications 1938 - 1974. Edited by Solomon Feferman. (Vol. 2 of 2). In deutscher Sprache. pages.
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Zustand: New. This second volume of a comprehensive edition of Kurt Godel's works collects the remainder of his published work, covering the period 1938-1974. (Volume I included all of his publications from 1929-1936). Each article or closely related group of articles is preceded by an introductory note that elucidates it and pl…aces it in historical context. Editor(s): Dawson, John. Num Pages: 432 pages, frontispiece, 5 halftone plates. BIC Classification: 3JJG; 3JJH; 3JJP; HPCF; HPL; PBCD. Category: (P) Professional & Vocational. Dimension: 242 x 163 x 25. Weight in Grams: 727. . 1990. Hardback. . . . . Books ship from the US and Ireland.
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Zustand: New. This is the first volume of a comprehensive edition of the works of Kurt Godel, the most outstanding logician of the 20th century. Editor(s): Dawson, John W., Jr. Num Pages: 490 pages, frontispiece, halftones. BIC Classification: PBCD; PBX. Category: (P) Professional & Vocational. Dimension: 243 x 161 x 37. Weight…in Grams: 956. . 1986. Illustrated. hardcover. . . . . Books ship from the US and Ireland.
The Undecidable, Basic Papers On Undecidable Propositions, Unsolvable Problems And Computable Functions (Including) Five Papers From Godel, Including Godel's "On Undecidable Propositions Of Formal Mathematical Systems" Etc., With New Supplementary Material From Godel, And Turing's "On Computable Numbers." And "Systems Of Logic Based On Ordinals", Also New Supplementary Material From Kleene For His Two Papers
Martin Davis (Editor); Kurt Godel, Alonzo Church, Alan M. Turing, J. B. Rosser, Stephen C. Kleene, Emil Post; Signed Bookplate Of Hal Berghel
Sprache: Englisch
Verlag: Raven Press, Hewlett Ny 1965
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Hardcover. Zustand: Near Fine. Zustand des Schutzumschlags: Very Good. 1st Edition. 440 Pp. Blue Cloth, Gilt. First Or Early Printing, Book Is 3.2 Cm Thick (An Otherwise Identical Issue In Blue Cloth Is Also 3.2 Cm Thick, But A Later Reprint In Blue Cloth With A Different Typesetting Of Title Page And Completely Different Copyri…ght Page With Isbn And In An Unpriced And Different Dust Jacket Is 2.9 Cm Thick). Slight Usage; Book Near Fine, Dj Priced $9.75, Light Usage, A Few Short Closed Tears At Edges And Minute Losses At Corners. The Book Is An Anthology Of 17 Papers, Most Previously Published, But Including Previously Unpublished Lectures By Godel And An Unpublished Account By Post Of His Early Work, And With Supplementary Material Furnished By Godel And Keene. Signed Bookplate And Also The Name Stamp Of Hal Berghel, Professor Of Computer Science At The University Of Nevada, Las Vegas Where He Has Previously Served As Director Of Both The Schools Of Computer Science And Informatics, And As Associate Dean Of The College Of Engineering. He Created And Directed The First Cybersecurity Degree Programs (Bachelors, Masters And Phd) In Nevada In 2005. He Was The Founding Director Of The Identity Theft And Financial Fraud Research And Operations Center And Cybersecurity Research Center.
The Undecidable, Basic Papers On Undecidable Propositions, Unsolvable Problems And Computable Functions (Including) Five Papers From Godel, Including Godel's "On Undecidable Propositions Of Formal Mathematical Systems" Etc., With New Supplementary Material From Godel, And Turing's "On Computable Numbers." And "Systems Of Logic Based On Ordinals", Also New Supplementary Material From Kleene For His Two Papers
Martin Davis (Editor); Kurt Godel, Alonzo Church, Alan M. Turing, J. B. Rosser, Stephen C. Kleene, Emil Post; Signed Bookplate Of Hal Berghel
Sprache: Englisch
Verlag: Raven Press, Hewlett Ny 1965
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Hardcover. Zustand: Near Fine. No Jacket. 1st Edition. 440 Pp. Red Cloth, Gilt. First Or Early Printing, Book Is 3.2 Cm Thick (An Otherwise Identical Issue In Blue Cloth Is Also 3.2 Cm Thick, But A Later Reprint In Blue Cloth With A Different Typesetting Of Title Page And Completely Different Copyright Page With Isbn And In An U…npriced And Different Dust Jacket Is 2.9 Cm Thick). Slight Usage; Book Near Fine, Bumping To Lower Front Tip, No Dut Jacket, No Marks. The Book Is An Anthology Of 17 Papers, Most Previously Published, But Including Previously Unpublished Lectures By Godel And An Unpublished Account By Post Of His Early Work, And With Supplementary Material Furnished By Godel And Keene.
Verlag: ARMAND COLIN 1971
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Couverture rigide. Zustand: bon. R240069448: 1971. In-8. Relié. Etat d'usage, Couv. légèrement passée, Dos abîmé, Intérieur acceptable. 412 pages - coins frottés - dos partiellement manquant. . . . Classification Dewey : 510-Mathématiques.
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Wisconsin, The Association for Symbolic Logic, 1938-39. Lev8vo. Entire volume one of "Journal of Symbolic Logic" (i.e. number 1-4), March 1938, June 1938, October 1938, January 1939. Bound in blue half cloth with gilt lettering to spine. Crossed-out library paper-label to lower part of spine and top left corner of front board. T…wo library stamps (in Chinese) to verso of title page. Internally a very fine and clean copy of the entire volume. [Kleene:] Pp. 150-55. [Entire volume: IV, 212 pp.]. First printing Kleene's milestone paper in which Kleene's O (Ordial numbers), a recursive function, is introduced. In set theory and computability theory, Kleene's is a canonical subset of the natural numbers when regarded as ordinal notations."In the seventeenth century, Leibniz envisaged a universal language that would allow one to reduce mathematical proofs to simple computations. Then, during the nineteenth century, llgicians such as Charles Babbage, Boole, Frege and Peano tried to formalize mathematical reasoning by an "algebraization" of logic. Finally, [.] Gödel, Church and Stephen Kleene introduced the notion of recursive functions. (The Princeston Companion to Mathematics. P. 111).The volume also contains the following papers of interest:1. Quine, W. V. Completeness of the propositional calculus. Pp. 37-402. Quine, W. V. On the theory of types. Pp. 125-39.3. Church, Alonzo. Additions and corrections to A bibliography of symbolic logic. Pp. 178-92.
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Kleene, Stephen C. (1909-94); Martin Davis (1928-2023). Collection of correspondence and other materials, consisting of: (1) 8 typed letters signed from Kleene to Davis. 8 sheets total. 1950-52. (2) Autograph letter signed from Davis to Kleene plus 2 draft versions of another of Davis's letters to Kleene. 15 sheets total. 1951-5…2. (3) Davis. Some preliminary remarks on recursively enumerable sets. Typed and autographed draft. 25 sheets total. N.d. [1952]. (4) Rice, Henry Gordon (1920-2003). Classes of enumerable sets and their decision problems. Offprint from Transactions of the American Mathematical Society 74 (1953). 358-366pp. 255 x 179 mm. Original printed wrappers, vertically creased, light soiling. Some creasing, soiling and marginal fraying, but very good. Complete listing available. "Kleene, along with Rózsa Peter, Alan Turing, Emil Post and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism" (Wikipedia article on Kleene). We are offering a collection of correspondence (plus related materials) between Kleene and Martin Davis, a mathematician and logician who made important contributions to computability theory. Davis's work on Hilbert's tenth problem-asking for a general algorithm to decide the solvability of Diophantine equations-led to the Matiyasevich-Robinson-Davis-Putman (MRDP) theorem implying that a solution to this problem is impossible. In No. 1 (see the calendar below), dated 26 April 1950, Kleene warned Davis of an error in his (Kleene's) 1944 paper "On the forms of the predicates in the theory of constructive ordinals," and expresses "the hope that nothing in the part of your thesis concerning the transfinite extension of the hierarchy of predicate forms depends on my alleged theorem that a O is expressible in the form (x) (Ey) R (A, x, y) . . ." Nos. 2 - 7, written between March and October 1952, center on Davis's "Arithmetical problems and recursively enumerable predicates," a paper he had submitted earlier that year to the Journal of Symbolic Logic, of which Kleene was the editor. The JSL had sent the paper to a referee for review (per Kleene's letter to Davis of 18 April), which, as Davis informed Kleene, "is giving rise to one of those rather futile author-referee wrangles I have heard so much about . . . I replied to the original referee's report claiming that his proof was incorrect as I had been unable to fill in several gaps in his proposed argument. The referee counter-replied showing me how the gaps might be filled in; his argument now seems to me to be correct. There remain, then, two questions: 1) Is the referee's proof superior to mine? 2) If so, in what form should it be published? . . ." On 7 May Kleene replied that "we shall easily settle the author-referee wrangle . . . I shall simply submit the paper, together with the first referee's reports, to an experienced second referee and take his verdict." This 7 May letter (no. 5) also includes some discussion of Davis's work compared to Kleene's own: "In regard to publication of the material from the second section of your thesis, it is a little hard to advise you. For one thing, of course, there is some question of competition between your material and mine . . . Until I have seen the mimeographed student notes on the course which you are giving, I will not know whether your development is substantially different from developments that are in the literature or will be in the literature when and if I succeed in getting my book [Introduction to Metamathematics] published . . ." On 4 June (No. 6) Kleene informed Davis that "I now have the second referee's report on your paper . . . I am returning the manuscript to you, for you to revise in accordance with the referee's suggestions." On 2 October, per Kleene's letter of that date (No. 7), Davis's paper was sent to the first referee for a final check. Nos. 8 - 12, written in January and February 1952, concern a report that Davis was preparing at Kleene's request on H. G. Rice's "Classes of recursively enumerable sets and their decision problems," a paper Rice had submitted to the JSL. "You will recall that I mentioned to you at the Bryn Mawr meetings (or was it Providence?) that, owing to the fact our pages are very crowded now, and the length of the paper of H. G. Rice, we may wish to transfer it. Under these circumstances it is embarrassing to us to hold it too long before raising this question with the author . . . Could I have [your] report within the next week . . ." (letter of 29 January). Davis replied on 3 February: "Although I told you at Providence, that I would let you have my report very soon, I am afraid that it is not yet ready. There are two reasons for this. The first of these is that my initial reading of the paper convinced me that it should be revised considerably before publication. As a result a more detailed report will be required than would ordinarily have been necessary . . ." By 18 February, per Kleene's letter of that date (no. 12), Davis had sent in his "exceedingly careful and thorough report" (No. 11), which recommended that Rice's paper "be rewritten with Parts II and IV omitted." A copy of Rice's paper is included with this collection. .
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Kleene, Stephen C. (1909-94); Martin Davis (1928-2023). (1) Group of 16 letters, including 8 typed letters signed and two autograph letters signed, pertaining to Kleene's 1981 paper, "Origins of recursive function theory," and Davis's 1982 paper, "Why Gödel didn't have Church's thesis"; see calendar of letters below. 26 sheets t…otal. October 1981 - 19 February 1982. Very good. (2) Kleene. Origins of recursive function theory. Offprint from Annals of the History of Computing 3 (1981). 52-67pp. 282 x 213 mm. Original plain wrappers. Very good. With 4 corrections in Kleene's hand. "Kleene, along with Rózsa Peter, Alan Turing, Emil Post and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism" (Wikipedia article on Kleene). We are offering a collection of correspondence between Kleene and Martin Davis, a mathematician and logician who made important contributions to computability theory. Davis's work on Hilbert's tenth problem-asking for a general algorithm to decide the solvability of Diophantine equations-led to the Matiyasevich-Robinson-Davis-Putman (MRDP) theorem implying that a solution to this problem is impossible. Both Kleene and Davis had studied under Alonzo Church at Princeton, Kleene in the 1930s and Davis in the 1940s. The correspondence offered here, consisting of 16 letters (see the calendar below), centers on Davis's paper, "Why Gödel didn't have Church's thesis" (Information and Control 54 [1982]: 3-24), which had been inspired by Kleene's 1979 lecture on "Origins of recursive function theory" given in San Juan, Puerto Rico in 1979 at the 20th annual IEEE Symposium on Foundations of Computer Science. In his letter of 11/14/79 (letter 1), Kleene proposed an addition to the published version of his lecture (Annals of the History of Computing 3 [1981]: 52-67), based on a suggestion by Davis: "What would you think of adding the following to the second full paragraph of the of the right column of page 378: In a conversation at San Juan on October 31, 1979, Davis . . . expressed to me the opinion that my proof of the equivalence of my definition of general recursiveness to Gödel's (which Gödel called 'not quite trivial'), and my normal form theorem, were considerations which combined with Turing's arguments to convince Gödel of the Church-Turing thesis . . ." Sometime in 1981 Davis sent Kleene a preliminary version of "Why Gödel didn't have Church's thesis"-a paper "directly stimulated by your San Juan lecture"-which outlined the development of -definability and recursive function theory by Gödel, Church, Turing, Kleene, Post and others in the 1930s. Davis asked for Kleene's comments and corrections to the paper (letter 2); Kleene ended up sending Davis two long letters (letters 4 and 9) with extensive criticisms and additions, clarifying the chronology and priority of discovery, and adding important historical detail, particularly with regard to Church and Gödel. An example: "Just how far back Church's expressed speculations [re -definability] went I don't definitely recall. But his definite proposal was after his speaking out on the significance of -definability as a number-theoretic notion in the fall of 1933 . . . Then one day in his office in Fine Hall he made the definite proposal. This had to be after December 1933 since I was away from Princeton from early September 1933 till sometime in January or February 1934 . . . And Church, who is very careful, in his letter of November 29, 1935 (copy enclosed), written when his memory of the period should have been reasonably fresh, puts '[his] proposal that lambda-definability be taken as a definition of [effective calculability] ahead of Gödel's introduction of general recursiveness' (letter 4, 10/22/81). Kleene's letter enclosed a photocopy of Church's 1935 letter (letter 6), in which Church described his and Kleene's development of -definability ("The notion of lambda-definability in its present form is, of course, the result of a gradual development . . . we seem to be agreed that the statement that the notion of lambda-definability is jointly due to you and me is fair . . .") and gave a brief history of "Gödel and the notions of recursiveness and effective calculability." In his letter of 11/16/81 (letter 9) Kleene supplied further information about Gödel's role vis-à-vis lambda-calculus and recursiveness theory, particularly his failure to credit Church's and Kleene's work: "Now, I hate to say it. But I must acknowledge feeling that Gödel was somewhat less than generous in acknowledging (except only, so far as I know, for the footnote on your p. 72) a role of Church or me in three matters. "In the spring term of 1934, Church had pushed -definability at a reluctant Gödel . . . Was it hard for Gödel to admit that Church had in fact been right (though not a persuasive as Turing later was), given Gödel's acceptance of Turing's equivalent? "As my second illustration of Gödel's reluctance to give credit, Gödel has never to my knowledge taken any public notice of my having a role in generalizing his (first) incompleteness theorem . . . "A third-rather trifling-illustration is the notion of 'partial recursive function.' I remember so vividly the words of Gödel on an occasion in Princeton in 1939-40 . . . when in a conversation with him I mentioned 'partial recursive functions' (terminology which, as you well know, I introduced in the J.S.L. in 1938). His exact words were, I swear, 'What is a parti.
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Kleene, Stephen C. (1909-94). Collection of 28 offprints, pamphlets, etc. on mathematical logic, as listed below. 1936-81. Various sizes; the largest measuring 282 x 215 mm. Original wrappers except as noted below. Occasional staining and wear, but very good; see list for condition details. From the library of Martin Davis (1928…-2023), with two of the offprints bearing his signature. 1. A note on recursive functions. Offprint from Bulletin of the American Mathematical Society (1936). 544-546pp. Original printed wrappers, small stain on front wrapper. Davis's ownership signature. 2. Review of Carnap's The Logical Syntax of Language. Offprint from The Journal of Symbolic Logic 4 (1939). 82-87pp. Original printed wrappers. Offprint of R. Carnap's "Remarks on 'Logical Syntax of Language'" (Introduction to Semantics, Harvard U. P., 1942) laid in. 3. (with H. P. Evans) A postulational basis for probability. Offprint from American Mathematical Monthly 46 (1939). 141148pp. Original printed wrappers. 4. On the forms of the predicates in the theory of constructive ordinals. Offprint from American Journal of Mathematics 66 (1944). 41-58pp. Original printed wrappers, stained, wrappers splitting at spine. Davis's ownership signature. 5. On the intuitionist logic. Offprint from Library of the Xth International Congress of Philosophy (Amsterdam, August 1118, 1948), Proceedings of the Congress (1949). 185-187pp. Original printed wrappers. 6. Recursive functions and intuitionist mathematics. Offprint from Proceedings of the International Congress of Mathematicians (1950). 679-685pp. Original printed wrappers. 7. A symmetric form of Gödel's theorem. Offprint from Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings 53 (1950). 244-246pp. Bifolium; without wrappers as issued. 8. Two papers on the predicate calculus. Memoirs of the American Mathematical Society, no. 10 (1952). 68pp. Original printed wrappers, ink stains on front wrapper. 9. Hierarchies of number-theoretic predicates. Offprint from Bulletin of the American Mathematical Society 61 (1955). 193-213pp. Original printed wrappers. 10. Arithmetic predicates and function quantifiers. Offprint from Transactions of the American Mathematical Society 79 (1955). 312-340pp. Original printed wrappers. 11. A note on computable functionals. Offprint from Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, series A (1956). 275-280pp. Without wrappers as issued. 12. (with J. W. Addison) A note on function quantification. Offprint from Proceedings of the American Mathematical Society 8 (1957). 1002-1006pp. Original printed wrappers. 13. Extension of an effectively generated class of functions by enumeration. Offprint from Colloquium mathematicum 6 (1958). 67-78pp. Without wrappers as issued. 14. Countable functionals. Offprint from Constructivity in Mathematics: Proceedings of the Colloquium Held at Amsterdam, 1957 (1959). 81-100pp. Without wrappers as issued. 15. Recursive functionals and quantifiers of finite types I. Offprint from Transactions of the American Mathematical Society 91 (1959). 52pp. Original printed wrappers. 16. Quantification of number-theoretic functions. Offprint from Composito mathematica 14 (1959). 23-40pp. Original printed wrappers. 17. Herbrand-Gödel-style recursive functionals of finite types. Offprint from Recursive Function Theory: Proceedings of Symposia in Pure Mathematics 5 (1962). 4975pp. Original printed wrappers. 18. Lambda-definable functionals of finite types. Offprint from Fundamenta mathematica 50 (1962). 281-303pp. Without wrappers as issued. 19. Disjunction and existence under implication in elementary intuitionistic formalisms. Offprint from Journal of Symbolic Logic 27 (1963). 11-18pp. 20. An addendum. Offprint from Journal of Symbolic Logic 28 (1963). 154-156pp. Original printed wrappers. 21. Recursive functionals and quantifiers of finite types II. Offprint from Transactions of the American Mathematical Society 108 (1963). 106-142pp. Original printed wrappers. 22. Classical extensions of intuitionist mathematics. Offprint from Proceedings of the 1964 International Congress for Logic, Methodology and Philosophy of Science, Held in Jerusalem, August 26-September 2, 1964 (1965). 31-44pp. 23. Logical calculus and realizability. Offprint from Acta philosophica fennica, fasc 18 (1965). 71-80pp. Original printed wrappers. 24. Constructive functions in "The Foundations of Intuitionistic Mathematics." Offprint from Logic, Methodology and Philosophy of Sciences 3 (1968). 137-144pp. Without wrappers as issued. 25. [Replacement page for] Formalized Recursive Functionals and Formalized Realizability, American Mathematical Society, memoir no. 89 (1969). P. 70. Single sheet, printed on gummed paper. 26. The work of Kurt Gödel. Offprint from Journal of Symbolic Logic 41 (1976). 761-778pp. Original printed wrappers. 27. An addendum to "The work of Kurt Gödel." Offprint from Journal of Symbolic Logic 43 (1978). P. 613. Original printed front wrapper; without back wrapper as issued. 28. The theory of recursive functions, approaching its centennial. Offprint from Bulletin (New Series) of the American Mathematical Society 5 (1981). 43-61pp. Original printed wrappers. .
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Wisconsin, The Association for Symbolic Logic, 1938-39. Lev8vo. Bound in red half cloth with gilt lettering to spine. In "Journal of Symbolic Logic", Volume 3 & 4 bound together. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. A very fine copy. [Kleene:] Pp. 150-55. [Entire volume: 4, 212, (4…), 194, (2) pp.]. First printing Kleene's milestone paper in which Kleene's O (Ordial numbers), a recursive function, is introduced. In set theory and computability theory, Kleene's is a canonical subset of the natural numbers when regarded as ordinal notations."In the seventeenth century, Leibniz envisaged a universal language that would allow one to reduce mathematical proofs to simple computations. Then, during the nineteenth century, llgicians such as Charles Babbage, Boole, Frege and Peano tried to formalize mathematical reasoning by an "algebraization" of logic. Finally, [.] Gödel, Church and Stephen Kleene introduced the notion of recursive functions. (The Princeston Companion to Mathematics. P. 111).The volume also contains the following papers of interest:1. Quine, W. V. Completeness of the propositional calculus. Pp. 37-402. Quine, W. V. On the theory of types. Pp. 125-39.3. Church, Alonzo. Additions and corrections to A bibliography of symbolic logic. Pp. 178-92.
