basic constructions:
strong axioms
further
natural deduction metalanguage, practical foundations
type theory (dependent, intensional, observational type theory, homotopy type theory)
computational trinitarianism =
propositions as types +programs as proofs +relation type theory/category theory
This entry collects links related to the book
Stefania Centrone, Deborah Kant, Deniz Sarikaya (editors):
Reflections on the Foundations of Mathematics
Synthese Library, vol 407.
Springer, Cham. 12 November 2019.
[ISBN:978-3-030-15654-1, doi:10.1007/978-3-030-15655-8]
Part I: Current Challenges for the Set-Theoretic Foundations
Mirna Džamonja, Deborah Kant, Interview With a Set Theorist [pdf, pdf]
Laura Fontanella, How to Choose New Axioms for Set Theory? [pdf]
Claudio Ternullo, Maddy On The Multiverse [pdf]
Philip Welch, Proving Theorems from Reflection [pdf]
Part II: What Are Homotopy Type Theory and the Univalent Foundations?
Thorsten Altenkirch, Naïve Type Theory [pdf]
Benedikt Ahrens, Paige Randall North, Univalent Foundations and the Equivalence Principle [arXiv:2202.01892]
Ulrik Buchholtz, Higher Structures in Homotopy Type Theory [arXiv:1807.02177]
Anthony Bordg, Univalent Foundations and the UniMath Library [arXiv:1710.02723]
Andrei Rodin, Models of HoTT and the Constructive View of Theories [pdf]
Part III: Comparing Set Theory, Category Theory, and Type Theory
Neil Barton, Sy-David Friedman, Set Theory and Structures [pdf]
Mirna Džamonja, A New Foundational Crisis in Mathematics, Is It Really Happening? [arXiv:1802.06221]
Ansten Klev, A Comparison of Type Theory with Set Theory [pdf]
Penelope Maddy, What Do We Want a Foundation to Do? Comparing Set-Theoretic, Category-Theoretic, and Univalent Approaches [pdf]
Part IV: Philosophical Thoughts on the Foundations of Mathematics
Merlin Carl, Formal and Natural Proof: A Phenomenological Approach [draft, pdf]
Michèle Friend, Varieties of Pluralism and Objectivity in Mathematics Varieties_of_Pluralism_and_Objectivity_in_Mathematics.pdf?
Last revised on January 12, 2024 at 02:12:51. See the history of this page for a list of all contributions to it.