User Joel David Hamkins

19 votes

3 answers

1k views

The arithmetic progression game and its variations: can you find optimal play?

asked Apr 10, 2018 at 0:03

19 votes

2 answers

3k views

What is the winning strategy in this pebble game?

asked Feb 27, 2020 at 12:02

19 votes

2 answers

1k views

Is the theory of a partial order bi-interpretable with the theory of a pre-order?

asked Jul 30, 2022 at 0:07

18 votes

0 answers

895 views

Is the universality of the surreal number line a weak global choice principle?

asked Jan 7, 2016 at 6:01

17 votes

1 answer

876 views

Which finitely presented groups can be distinguished by decidable properties?

asked Mar 5, 2010 at 3:40

17 votes

9 answers

4k views

How should the Math Subject Classification (MSC) be revised or improved?

asked Jun 16, 2010 at 2:24

17 votes

2 answers

2k views

Do the surreal numbers enjoy the transfer principle in ZFC?

asked Nov 25 at 3:34

16 votes

2 answers

1k views

Are the vertical sections of the Ackermann function primitive recursive?

asked Dec 12, 2020 at 10:53

16 votes

1 answer

1k views

Can there be a global linear ordering of the universe without a global well-ordering of the universe?

asked Nov 3, 2012 at 12:37

16 votes

1 answer

841 views

Do all countable $\omega$-standard models of ZF with an amorphous set have the same inclusion relation up to isomorphism?

asked Apr 17, 2017 at 0:37

16 votes

1 answer

751 views

Is it consistent with ZFC that no nontrivial forcing notion has automatic mutual genericity?

asked Nov 4, 2015 at 3:11

16 votes

1 answer

1k views

Is there a nonstandard model of arithmetic having precisely one inductive truth predicate?

asked Nov 11, 2014 at 13:35

15 votes

3 answers

717 views

Does every set $X$ have a topology for which the only continuous self-surjection is the identity map?

asked Aug 13, 2015 at 3:47

15 votes

1 answer

987 views

Does every model of ZF-foundation have an extension, with no new well-founded sets, where every set is bijective with a well-founded set?

asked May 15, 2018 at 13:29

15 votes

2 answers

919 views

Which are the hereditarily computably enumerable sets?

asked Jun 22 at 13:15

14 votes

2 answers

1k views

If every definable class admits a group structure, must global choice hold?

asked Jul 25 at 21:18

14 votes

1 answer

607 views

Is there an elementary proof of a better result for the finite guessing-box puzzle?

asked Aug 2 at 13:38

14 votes

1 answer

822 views

Can a model of set theory be realized as a Cohen-subset forcing extension in two different ways, with different grounds and different cardinals?

asked Feb 1, 2013 at 20:43

13 votes

1 answer

973 views

Does every feasible partial order relation on the natural numbers extend to a feasible linear order relation?

asked Feb 27, 2012 at 14:27

13 votes

1 answer

751 views

Is there a class of mathematical structures with non-isomorphic natural representations as a standard Borel space?

asked Mar 26, 2016 at 22:57

12 votes

3 answers

1k views

If Q is a subset of the plane of size less than continuum, then does every closed F in Q extend to a closed connected G in the plane with the same trace on Q? (Or is this independent of ZFC?)

asked Nov 16, 2010 at 20:01

12 votes

2 answers

903 views

Can there be an almost-special not-fully-special Aronszajn tree?

asked Mar 26, 2012 at 7:31

12 votes

1 answer

780 views

Does every countable set of Turing degrees have an upper bound, without AC?

asked Apr 19, 2021 at 16:01

12 votes

3 answers

888 views

Is there a simple instance of intransitivity for implicit definability?

asked Jul 10, 2022 at 12:33

11 votes

1 answer

711 views

Can we separate the almost-disjointness sunflower numbers?

asked Jun 10, 2021 at 8:08

11 votes

2 answers

1k views

An infinite hat puzzle variation—if we don't know our place, can we still be almost all correct?

asked Jul 31 at 2:29

11 votes

2 answers

668 views

What is the computational-complexity-theoretic analogue of computable inseparability? For example, if P is not NP, are there disjoint NP sets with no separation in P?

asked Feb 29, 2012 at 13:37

10 votes

1 answer

465 views

If $\kappa$ is weakly inaccessible and $A\subset\kappa$, can $L[A]$ violate $\kappa^{\lt\kappa}=\kappa$?

asked Mar 16, 2015 at 0:23

10 votes

0 answers

381 views

Can one define in ZFC a directed system of embeddings on the class of all linear orders realizing the surreal line as the direct limit?

asked Nov 11, 2022 at 17:17

9 votes

1 answer

611 views

Does every cofinal branch through Kleene's O compute true arithmetic?

asked May 10, 2020 at 11:24

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104 Questions

The arithmetic progression game and its variations: can you find optimal play?

What is the winning strategy in this pebble game?

Is the theory of a partial order bi-interpretable with the theory of a pre-order?

Is the universality of the surreal number line a weak global choice principle?

Which finitely presented groups can be distinguished by decidable properties?

How should the Math Subject Classification (MSC) be revised or improved?

Do the surreal numbers enjoy the transfer principle in ZFC?

Are the vertical sections of the Ackermann function primitive recursive?

Can there be a global linear ordering of the universe without a global well-ordering of the universe?

Do all countable $\omega$-standard models of ZF with an amorphous set have the same inclusion relation up to isomorphism?

Is it consistent with ZFC that no nontrivial forcing notion has automatic mutual genericity?

Is there a nonstandard model of arithmetic having precisely one inductive truth predicate?

Does every set $X$ have a topology for which the only continuous self-surjection is the identity map?

Does every model of ZF-foundation have an extension, with no new well-founded sets, where every set is bijective with a well-founded set?

Which are the hereditarily computably enumerable sets?

If every definable class admits a group structure, must global choice hold?

Is there an elementary proof of a better result for the finite guessing-box puzzle?

Can a model of set theory be realized as a Cohen-subset forcing extension in two different ways, with different grounds and different cardinals?

Does every feasible partial order relation on the natural numbers extend to a feasible linear order relation?

Is there a class of mathematical structures with non-isomorphic natural representations as a standard Borel space?

If Q is a subset of the plane of size less than continuum, then does every closed F in Q extend to a closed connected G in the plane with the same trace on Q? (Or is this independent of ZFC?)

Can there be an almost-special not-fully-special Aronszajn tree?

Does every countable set of Turing degrees have an upper bound, without AC?

Is there a simple instance of intransitivity for implicit definability?

Can we separate the almost-disjointness sunflower numbers?

An infinite hat puzzle variation—if we don't know our place, can we still be almost all correct?

What is the computational-complexity-theoretic analogue of computable inseparability? For example, if P is not NP, are there disjoint NP sets with no separation in P?

If $\kappa$ is weakly inaccessible and $A\subset\kappa$, can $L[A]$ violate $\kappa^{\lt\kappa}=\kappa$?

Can one define in ZFC a directed system of embeddings on the class of all linear orders realizing the surreal line as the direct limit?

Does every cofinal branch through Kleene's O compute true arithmetic?