en 1answer
Joel David Hamkins's questions - English 1answer
73 questions.
Questions
Answers
Which are the rigid suborders of the real line?
22
2
answers,
6
favourites,
875
views
set-theory
order-theory
gn.general-topology
lo.logic
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?)
11
3
answers,
1
favourites,
822
views
gn.general-topology
set-theory
forcing
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?
14
1
answers,
1
favourites,
495
views
set-theory
lo.logic
axiom-of-choice
mathematical-philosophy
The Sudoku game: Solver-Spoiler variation
9
3
answers,
2
favourites,
685
views
combinatorial-game-theory
sudoku
infinite-games
The arithmetic progression game and its variations: can you find optimal play?
19
3
answers,
7
favourites,
482
views
nt.number-theory
co.combinatorics
combinatorial-game-theory
infinite-games
Is there a universal countable group? (a countable group containing every countable group as a subgroup)
35
4
answers,
16
favourites,
2.912
views
gr.group-theory
Is the ultraproduct concept fundamentally category-theoretic?
47
7
answers,
23
favourites,
3.688
views
ct.category-theory
lo.logic
model-theory
set-theory
How big is the smallest nontrivial partition of the unit interval into closed disjoint closed sets? [duplicate]
5
0
answers,
0
favourites,
107
views
set-theory
gn.general-topology
Which graphs are Cayley graphs?
63
6
answers,
30
favourites,
6.278
views
gr.group-theory
graph-theory
set-theory
computability-theory
cayley-graphs
What are the most attractive Turing undecidable problems in mathematics?
110
44
answers,
98
favourites,
26.367
views
computability-theory
big-list
examples
lo.logic
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?
22
1
answers,
7
favourites,
713
views
set-theory
lo.logic
forcing
modal-logic
Does every set $X$ have a topology for which the only continuous self-surjection is the identity map?
15
3
answers,
2
favourites,
610
views
set-theory
gn.general-topology
For a computable binary tree, is having no computable branches the same as having no probabilistic algorithm for producing branches?
17
2
answers,
5
favourites,
742
views
lo.logic
computability-theory
When is a game tree the game tree of a board game?
17
5
answers,
5
favourites,
846
views
game-theory
combinatorial-game-theory
Finding a PA cut in a nonstandard model of PA
7
1
answers,
2
favourites,
406
views
lo.logic
model-theory
models-of-pa
Do all countable $\omega$-standard models of ZF with an amorphous set have the same inclusion relation up to isomorphism?
16
0
answers,
0
favourites,
424
views
lo.logic
set-theory
axiom-of-choice
Can there be an almost-special not-fully-special Aronszajn tree?
13
2
answers,
4
favourites,
766
views
set-theory
forcing
lo.logic
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?
21
6
answers,
6
favourites,
1.040
views
nonstandard-analysis
set-theory
lo.logic
models-of-pa
model-theory
Can the symmetric groups on sets of different cardinalities be isomorphic?
48
5
answers,
12
favourites,
3.557
views
gr.group-theory
set-theory
Does ZF+AD settle the original Suslin hypothesis?
24
3
answers,
7
favourites,
1.417
views
lo.logic
set-theory
Is $n$ uniformly computable from an oracle for the $n^{\rm th}$ jump $0^{(n)}$?
4
1
answers,
0
favourites,
209
views
lo.logic
computability-theory
Can $V\neq\text{HOD}$ if every $\Sigma_2$-definable set has an ordinal-definable element?
7
1
answers,
3
favourites,
530
views
lo.logic
set-theory
definability
Does War have infinite expected length?
66
10
answers,
11
favourites,
14.602
views
co.combinatorics
pr.probability
recreational-mathematics
game-theory
Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just from the program?
28
3
answers,
6
favourites,
1.854
views
computability-theory
computational-complexity
lo.logic
np
Are the definable hyper-reals, using quantifiers only over the standard reals and natural numbers, the same as the algebraic numbers?
8
1
answers,
0
favourites,
345
views
lo.logic
model-theory
nonstandard-analysis
definability
Is there a dense subset of the real plane with all pairwise distances rational?
84
5
answers,
29
favourites,
7.230
views
discrete-geometry
How should the Math Subject Classification (MSC) be revised or improved?
17
9
answers,
6
favourites,
2.565
views
msc
soft-question
big-list
Is the sphere the only surface all of whose projections are circles? Or: Can we deduce a spherical Earth by observing that its shadows on the Moon are always circular?
72
4
answers,
35
favourites,
7.486
views
geometry
mg.metric-geometry
What is the optimal size in the finite axiom of symmetry?
10
3
answers,
1
favourites,
637
views
co.combinatorics
Is there a class of mathematical structures with non-isomorphic natural representations as a standard Borel space?
14
1
answers,
5
favourites,
568
views
lo.logic
set-theory
measure-theory
descriptive-set-theory
mathematical-philosophy
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