User godelian

69 votes

Examples of unexpected mathematical images

answered Aug 9, 2014 at 8:52

33 votes

Elementary applications of Krein-Milman

answered May 19, 2012 at 21:28

33 votes

Accepted

Does the "three-set-lemma" imply the Axiom of Choice?

answered Apr 20, 2020 at 14:00

22 votes

Accepted

Which failed attempts have there been to find a contradiction in ZFC or ZF?

answered Jul 19, 2019 at 19:19

22 votes

Category of categories as a foundation of mathematics

answered Feb 15, 2011 at 21:07

21 votes

Does the original 1931 proof of Gödel’s incompleteness rely on the completeness theorem, or is it purely syntactic?

answered Apr 23 at 13:01

20 votes

Accepted

Existence of prime ideals and Axiom of Choice.

answered Jun 1, 2012 at 10:06

17 votes

Accepted

Corollaries of the Yoneda Lemma in Analysis?

answered Jul 3, 2016 at 0:10

15 votes

Accepted

Henkin-style completeness proofs for intuitionistic logic

answered Jan 6, 2019 at 0:20

13 votes

Accepted

Intuition for pseudo-points and the inductive step in Johnstone's proof of Deligne's completeness theorem

answered Oct 21, 2018 at 10:52

13 votes

Old books you would like to have reprinted with high-quality typesetting

answered Dec 17, 2018 at 13:34

13 votes

Accepted

Is there an infinite-dimensional Banach space with a compact unit ball?

answered Oct 10, 2011 at 23:13

12 votes

Software and ideas for workshops and conferences with long-distance participants

answered Dec 28, 2019 at 19:37

12 votes

Accepted

Deductive system involving only geometric sequents

answered Mar 28, 2022 at 18:58

12 votes

Accepted

Has Goedel's Second Incompleteness Theorem been proven using Lawvere's Fixed Point Theorem?

answered Jun 10, 2022 at 11:45

10 votes

In which categories is the union of subobjects given by the pushout over the intersection?

answered Dec 24, 2022 at 20:25

10 votes

Can the Riemann hypothesis be undecidable?

answered Nov 1, 2011 at 16:37

9 votes

What "metatheory" did early set theory/logic researchers use to prove semantic results?

answered Apr 16, 2018 at 9:44

8 votes

Grothendieck toposes and logic

answered Jun 6, 2017 at 14:38

7 votes

A question regarding the Hahn-Banach theorem

answered Jan 9, 2015 at 16:33

7 votes

Accepted

A list of proofs of "Coherent topoi have enough points"

answered Aug 21, 2019 at 15:44

7 votes

construction of nonmeasurable sets

answered Aug 29, 2014 at 16:51

7 votes

Accepted

Countable unions and the axiom of countable choice

answered Sep 18, 2011 at 0:46

6 votes

Problems where we can't make a canonical choice, solved by looking at all choices at once

answered Feb 17, 2011 at 16:06

6 votes

Accepted

Why does the category of definable sets of $T^\mathrm{eq}$ have coproducts?

answered Mar 20, 2022 at 13:21

6 votes

Accepted

Joyal arithmetic universes and the Box operator

answered Jul 3, 2022 at 21:50

5 votes

Notable examples of syntactic proofs whose existence is guaranteed by completeness, but having been found later than a semantic proof?

answered Jul 19, 2017 at 9:52

5 votes

Is it possible to formulate the axiom of choice as the existence of a survival strategy?

answered Oct 15, 2014 at 0:14

4 votes

Awfully sophisticated proof for simple facts

answered Jun 19, 2011 at 19:17

4 votes

Generalizing contour integration to quaternions and bicomplex numbers

answered Mar 3, 2021 at 23:02

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41 Answers

Examples of unexpected mathematical images

Elementary applications of Krein-Milman

Does the "three-set-lemma" imply the Axiom of Choice?

Which failed attempts have there been to find a contradiction in ZFC or ZF?

Category of categories as a foundation of mathematics

Does the original 1931 proof of Gödel’s incompleteness rely on the completeness theorem, or is it purely syntactic?

Existence of prime ideals and Axiom of Choice.

Corollaries of the Yoneda Lemma in Analysis?

Henkin-style completeness proofs for intuitionistic logic

Intuition for pseudo-points and the inductive step in Johnstone's proof of Deligne's completeness theorem

Old books you would like to have reprinted with high-quality typesetting

Is there an infinite-dimensional Banach space with a compact unit ball?

Software and ideas for workshops and conferences with long-distance participants

Deductive system involving only geometric sequents

Has Goedel's Second Incompleteness Theorem been proven using Lawvere's Fixed Point Theorem?

In which categories is the union of subobjects given by the pushout over the intersection?

Can the Riemann hypothesis be undecidable?

What "metatheory" did early set theory/logic researchers use to prove semantic results?

Grothendieck toposes and logic

A question regarding the Hahn-Banach theorem

A list of proofs of "Coherent topoi have enough points"

construction of nonmeasurable sets

Countable unions and the axiom of countable choice

Problems where we can't make a canonical choice, solved by looking at all choices at once

Why does the category of definable sets of $T^\mathrm{eq}$ have coproducts?

Joyal arithmetic universes and the Box operator

Notable examples of syntactic proofs whose existence is guaranteed by completeness, but having been found later than a semantic proof?

Is it possible to formulate the axiom of choice as the existence of a survival strategy?

Awfully sophisticated proof for simple facts

Generalizing contour integration to quaternions and bicomplex numbers