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Philosophy of set theory and mathematics
Recommended reading
Topic 4: Concepts of infinity: logic vs mathematics
Concepts of inifity
Concepts of inifity
Conditions d'achèvement
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Concepts of inifity
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◄ Zach: The significance...
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Hilbert: On the infinite
Moore: Hilbert on the infinite and set theory
Benacerraf, Putnam - Philosophy of mathematics
Reflections on the foundations of mathematics
Does mathematics need new axioms?
Shapiro - Oxford handbook of philosophy of mathematics and logic
Judah, Just, Woodin (Eds): Set theory of the continuum
Mac Lane: Categorical algebra and set-theoretic foundations
Macintyre: Model theory: Geometrical and set-theoretic aspects and prospects
Baldwin: The Dividing Line Methdology
Maddy I
Maddy II
H. Putnam: Mathematics without foundations
Extra reading: H. Putnam: What is mathematical truth
M. Balaguer: A Platonist Epistemology
Extra reading (the paper Balaguer responds to): [Benacerraf] - Mathematical truth
Zach: Hilbert's programme
(Further reading) Smorynski: Hilbert's programme
(Further reading) epsilon-calculus + Herbrand's theorem
Sommer: Transfinite induction in PA (APAL)
Category theory, Awodey
Marquis - Review of Symbolic Logic
Feferman's paper
Marquis - Synthese
Lambda-calculus
Type theory
Intuitionistic Type Theory (Homotopy T. Theory, sec 7.2.)
Wadler: Propositions as Types
AMS survey: Voevodsky’s Univalence Axiom in Homotopy Type Theory
[Woodin] - CH - popular explanation - part I (Notices of AMS)
[Woodin] - CH - popular explanation - part II (Notices of AMS)
V. Kolman: Introduction to "On bad infinity"
[Brouwer] - Intuitionism and formalism (1913, BAMS)
[Detlefsen] - On interpeting second Goedel theorem 1979 (JPL)
[Feferman, Friedman, Maddy, Steel]-Does mathematics need new axioms? BSL (2000)
[Antos, Friedman, Honzik, Ternullo] Multiverse conceptions in set theory
[Hamkins]-Set-theoretic-multiverse 2012 (RSL)
[Shelah] Logical Dreams
Book on connections between mathematics and set theory- [Ferreiros] - Labyrinth of Thought
Indespensability Arguments
Cutland: Non-standard measure theory and its applications
Propositions as Types
Zach: The significance...