Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts By: Stefania Centrone, Deborah Kant, Deniz Sarikaya

Author: Stefania Centrone

Part Current Challenges for the Set Theoretic Foundations1. Neil Barton and Sy-David Does set theory need an apology?2. Laura The choice of new axioms in set theory3. Michèle Pluralism in Foundations of Oxymoron, Paradox, Neither or Both?4. Deborah A distinction between meta set theory and object set theory5. Jan von The weaknesses of set theory6. Claudio Multiversism and Naturalism7. Philip Proving Theorems from Global Reflection Theorems
Part What are the Univalent Foundations? (In Alphabetical order)8. Benedikt Ahrens and Paige Univalent foundations and the equivalence principle9. Thorsten A constructive justification of Homotopy Type Theory10. Ulrik Higher structures in Homotopy Type Theory11. Andrei Models of HoTT and the Semantic View of Theories12. Urs Modern Physics formalized in Modal Homotopy Type Theory13. Vladimir Multiple Concepts of Equality in the New Foundations of Mathematics
Part Thoughts on the Foundations of Mathematics14. Nathan Foundations for the working mathematician, and for their computer15. Merlin Formal and Natural Proof – A phenomenological approach16. Stefania Centrone and Deniz Thoughts on the Foundation of Logicism, Intuitionism and Formalism17. Mirna Dž A new foundational crisis in mathematics, is it really happening?18. Penelope What foundational jobs do we want done?19. Giovanni Dynamics in what does it mean in practice20. Roy Does mathematics need foundations?