Infinite Sets and Foundations (Joel David Hamkins) | Ep. 17
Joel David Hamkins is a Professor of Logic with appointments in Philosophy and Mathematics at Oxford University. His main interest is in set theory. We discuss the field of set theory: what it can say about infinite sets and which issues are unresolved, and the relation of set theory to philosophical issues concerning the foundations of mathematics.
Joel's website: http://jdh.hamkins.org
Joel's Youtube channel: / @joeldavidhamkins5484
Joel's post summarizing ongoing work in set theory: https://math.stackexchange.com/a/2556...
Joel's recent books:
Proof and the Art of Mathematics https://amzn.to/3DsjmFR
Lectures on the Philosophy of Mathematics https://amzn.to/3DlpPCJ
(these are my affiliate links)
Timestamps
0:00 Intro
2:11 Joel's background. Interaction between math and philosophy
9:04 Joel's work; infinite chess.
14:45 Infinite ordinals
22:27 The Cantor-Bendixson process
29:41 Uncountable ordinals
32:10 First order vs. second order theories
41:16 Non-standard analysis
46:57 The ZFC axioms and well-ordering of the reals
58:11 Showing independence of statements. Models and forcing.
1:04:38 Sets, classes, and categories
1:19:22 Is there one true set theory? Are projective sets Lebesgue measurable?
1:30:20 What does set theory look like if certain axioms are rejected?
1:36:06 How to judge philosophical positions about math
1:42:01 Concrete math where set theory becomes relevant. Tarski-Seidenberg on positive polynomials.
1:48:48 Goodstein sequences and the use of infinite ordinals
1:58:43 The state of set theory today
2:01:41 Joel's recent books
Check out my discussion with Norman Wildberger on whether to admit infinite sets to which we refer several times: • Math Debate: Real numbers and the inf...
Playlist of full episodes of this podcast: • Daniel Rubin Show, Full episodes
Also check out my Tricky Parts of Calculus series of lectures: • Tricky Parts of Calculus
![[FREE] Big Yavo Type Beat](https://images.mixrolikus.cc/video/ipZpeZuo4bE)
