User Joel David Hamkins

32 votes

9 answers

5k views

How many groups of size at most n are there? What is the asymptotic growth rate? And what of rings, fields, graphs, partial orders, etc.?

asked Apr 13, 2010 at 21:57

31 votes

3 answers

3k views

Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just from the program?

asked Jun 13, 2010 at 19:00

31 votes

6 answers

3k views

How can category theory help my research in set theory?

asked Nov 29, 2009 at 22:04

31 votes

3 answers

2k views

Is the Rado graph a Cayley graph? If so, what is the group like? (And other questions...)

asked Oct 25, 2010 at 19:10

31 votes

2 answers

2k views

Does Fermat's last theorem hold in the ordinals?

asked Dec 4, 2013 at 18:31

30 votes

3 answers

3k views

Can there be an embedding j:V → L, from the set-theoretic universe V to the constructible universe L, when V ≠ L?

asked Jul 10, 2012 at 2:37

29 votes

2 answers

1k views

Can a fixed finite-length straightedge and finite-size compass still construct all constructible points in the plane?

asked Jul 11, 2020 at 16:32

26 votes

1 answer

1k views

Can we find strong fixed-points in the fixed-point lemma of Gödel's incompleteness theorem, that is, where the fixed point is syntactically identical to its substitution instance rather than merely provably equivalent to it?

asked Dec 11, 2011 at 1:41

26 votes

4 answers

2k views

Does every set of reals contain a measure-zero set of the same cardinality? Does it contain a meager set of the same cardinality?

asked Oct 10, 2013 at 23:06

26 votes

3 answers

2k views

Does ZF+AD settle the original Suslin hypothesis?

asked Sep 17, 2017 at 3:11

25 votes

4 answers

2k views

The Chocolatier's game: can the Glutton win with a restricted form of strategy?

asked Aug 6, 2021 at 15:56

25 votes

2 answers

2k views

Is there a continuous partition of space into circles?

asked Oct 24 at 14:09

24 votes

2 answers

1k views

What is the complexity of the winning condition in infinite Hex? In particular, is infinite Hex a Borel game?

asked Nov 30, 2022 at 1:39

24 votes

2 answers

1k views

Which are the rigid suborders of the real line?

asked Dec 27, 2009 at 21:33

23 votes

4 answers

2k views

Can we recognize when a category is equivalent to the category of models of a first order theory?

asked Jan 27, 2010 at 17:55

22 votes

5 answers

1k views

What is the spectrum of possible cofinality types for cuts in an ordered field? Or in a model of the hyperreals? Or in a nonstandard model of arithmetic?

asked Aug 10, 2011 at 19:19

22 votes

1 answer

883 views

Is the axiom $\Diamond\Box\varphi\to\Box\Diamond\varphi$ in c.c.c. forcing potentialism equivalent to the productivity of c.c.c. forcing?

asked Feb 3, 2018 at 15:29

22 votes

4 answers

1k views

Is there a Leibnizian model with no definable elements, in a finite language?

asked May 7, 2015 at 18:12

22 votes

1 answer

1k views

Does greedy circle packing exhaust the measure of every bounded open set in the plane?

asked Mar 16 at 14:11

21 votes

1 answer

864 views

Is there a minimal (least?) countably saturated real-closed field?

asked Jul 12 at 2:02

21 votes

2 answers

1k views

What is the large cardinal strength of the assertion that every $\kappa$-complete filter on $\kappa$ extends to a $\kappa$-complete ultrafilter?

asked Jun 27, 2014 at 1:06

21 votes

2 answers

1k views

Is the union of a chain of elementary embeddings elementary?

asked Sep 10, 2019 at 15:46

20 votes

2 answers

1k views

For a computable binary tree, is having no computable branches the same as having no probabilistic algorithm for producing branches?

asked Dec 30, 2017 at 14:00

20 votes

1 answer

864 views

Is there a model of ZF set theory with a set that does not inject into the cardinals?

asked May 21, 2014 at 19:55

20 votes

1 answer

1k views

Is there a subset of the natural number plane, which doesn't know which of its slices are arithmetic?

asked Sep 5, 2013 at 22:49

20 votes

5 answers

2k views

Isomorphism types or structure theory for nonstandard analysis

asked Jan 4, 2010 at 5:05

20 votes

7 answers

2k views

Does every set admit a rigid binary relation? (and how is this related to the Axiom of Choice?)

asked Nov 20, 2009 at 13:25

19 votes

4 answers

1k views

Does every decidable question about finitely presented groups amount to a question about abelian groups?

asked Feb 26, 2010 at 17:36

19 votes

2 answers

1k views

Which graphs are elementarily equivalent to their own disjoint sums?

asked Aug 31, 2010 at 23:27

19 votes

5 answers

1k views

When is a game tree the game tree of a board game?

asked Dec 9, 2017 at 23:14

Stack Exchange Network

104 Questions

How many groups of size at most n are there? What is the asymptotic growth rate? And what of rings, fields, graphs, partial orders, etc.?

Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just from the program?

How can category theory help my research in set theory?

Is the Rado graph a Cayley graph? If so, what is the group like? (And other questions...)

Does Fermat's last theorem hold in the ordinals?

Can there be an embedding j:V → L, from the set-theoretic universe V to the constructible universe L, when V ≠ L?

Can a fixed finite-length straightedge and finite-size compass still construct all constructible points in the plane?

Can we find strong fixed-points in the fixed-point lemma of Gödel's incompleteness theorem, that is, where the fixed point is syntactically identical to its substitution instance rather than merely provably equivalent to it?

Does every set of reals contain a measure-zero set of the same cardinality? Does it contain a meager set of the same cardinality?

Does ZF+AD settle the original Suslin hypothesis?

The Chocolatier's game: can the Glutton win with a restricted form of strategy?

Is there a continuous partition of space into circles?

What is the complexity of the winning condition in infinite Hex? In particular, is infinite Hex a Borel game?

Which are the rigid suborders of the real line?

Can we recognize when a category is equivalent to the category of models of a first order theory?

What is the spectrum of possible cofinality types for cuts in an ordered field? Or in a model of the hyperreals? Or in a nonstandard model of arithmetic?

Is the axiom $\Diamond\Box\varphi\to\Box\Diamond\varphi$ in c.c.c. forcing potentialism equivalent to the productivity of c.c.c. forcing?

Is there a Leibnizian model with no definable elements, in a finite language?

Does greedy circle packing exhaust the measure of every bounded open set in the plane?

Is there a minimal (least?) countably saturated real-closed field?

What is the large cardinal strength of the assertion that every $\kappa$-complete filter on $\kappa$ extends to a $\kappa$-complete ultrafilter?

Is the union of a chain of elementary embeddings elementary?

For a computable binary tree, is having no computable branches the same as having no probabilistic algorithm for producing branches?

Is there a model of ZF set theory with a set that does not inject into the cardinals?

Is there a subset of the natural number plane, which doesn't know which of its slices are arithmetic?

Isomorphism types or structure theory for nonstandard analysis

Does every set admit a rigid binary relation? (and how is this related to the Axiom of Choice?)

Does every decidable question about finitely presented groups amount to a question about abelian groups?

Which graphs are elementarily equivalent to their own disjoint sums?

When is a game tree the game tree of a board game?