Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts - Softcover
Buch 248 von 304: Synthese Library
Inhaltsangabe
Part I: Current Challenges for the Set Theoretic Foundations
1. Neil Barton and Sy-David Friedman: Does set theory need an apology?
2. Laura Fontanella: The choice of new axioms in set theory
3. Michèle Friend: Pluralism in Foundations of Mathematics: Oxymoron, Paradox, Neither or Both?
4. Deborah Kant: A distinction between meta set theory and object set theory
5. Jan von Plato: The weaknesses of set theory
6. Claudio Ternullo: Multiversism and Naturalism
7. Philip Welch: Proving Theorems from Reflection: Global Reflection Theorems
Part II: What are the Univalent Foundations? (In Alphabetical order)
8. Benedikt Ahrens and Paige North: Univalent foundations and the equivalence principle
9. Thorsten Altenkirch: A constructive justification of Homotopy Type Theory
10. Ulrik Buchholtz: Title: Higher structures in Homotopy Type Theory
11. Andrei Rodin: Models of HoTT and the Semantic View of Theories
12. Urs Schreiber: Modern Physics formalized in Modal Homotopy Type Theory
13. Vladimir Voevodsky: Multiple Concepts of Equality in the New Foundations of Mathematics
Part III: Thoughts on the Foundations of Mathematics
14. Nathan Bowler: Foundations for the working mathematician, and for their computer
15. Merlin Carl: Formal and Natural Proof - A phenomenological approach
16. Stefania Centrone and Deniz Sarikaya: Thoughts on the Foundation of Mathematics: Logicism, Intuitionism and Formalism
17. Mirna Džamonja: A new foundational crisis in mathematics, is it really happening?
18. Penelope Maddy: What foundational jobs do we want done?
19. Giovanni Sambin: Dynamics in foundations: what does it mean in practice
20. Roy Wagner: Does mathematics need foundations?
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