#1
Vaught's Conjecture
!!!Very high impact — resolution would be of award-level significance#2
Martin's Conjecture
!!!Very high impact — resolution would be of award-level significance#3
Is Fraïssé's Conjecture Provable in ATR₀?
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#4
Stable Forking Conjecture
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#5
Does the Partition Principle imply the Axiom of Choice?
!!!Very high impact — resolution would be of award-level significance#6
Is the universal triangle free graph pseudofinite?
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#7
Kolmogorov-Loveland randomness vs Martin-Löf randomness
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#8
Conservativity of Ramsey's Theorem for pairs
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#9
Borel boundedness of CBERs
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#10
Is every Polish group graphic?
!Ordinary impact — every problem listed here is a genuine, worthwhile open problem#11
Kreisel's Conjecture
!Ordinary impact — every problem listed here is a genuine, worthwhile open problem#12
Weiss's Question
!!!Very high impact — resolution would be of award-level significance#13
Stable fields conjecture
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#14
Cherlin-Zilber Algebraicity Conjecture
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#15
Axiomatizability of generic automorphisms
!Ordinary impact — every problem listed here is a genuine, worthwhile open problem#16
Axiom of Choice and bases for vector spaces over a specific field
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#17
Non-trivial automorphisms of the Turing degrees
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#18
Scott sets and standard systems of models of PA
!Ordinary impact — every problem listed here is a genuine, worthwhile open problem#19
Hilbert's Tenth Problem over Q
!!!Very high impact — resolution would be of award-level significance#20
Essentially countable isomorphism relations of first order theories
!Ordinary impact — every problem listed here is a genuine, worthwhile open problem#21
Sacks's Conjecture on embedding partial orders in the Turing degrees
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#22
Borel Ruziewicz problem
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#23
Superpolynomial bounds on Frege proofs
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)#24
Is add(N) < add(UN) consistent?
!Ordinary impact — every problem listed here is a genuine, worthwhile open problem#25
The increasing union problem for CBERs
!!High impact — resolution would likely be publishable in a top journal (Advances-level or above)