4 problems

The conjecture that Martin's Axiom is unnecessary for most quotient lifting results
arXiv@arxiv
Let $\operatorname{{\mathsf {MA}_{\aleph_1}}}$ denote Martin's Axiom at level $\aleph_1$ . Quotient-structure lifting results are results asserting that suitable homomorphisms or au…
Conjecturesolvedforcing quotient-structures set-theory
1
The forcing-absoluteness conjecture for non-isomorphic Borel quotients
arXiv@arxiv
Non-isomorphism absoluteness conjecture. If ${\mathcal M}/E$ and ${\mathcal N}/F$ are non-isomorphic in some forcing extension, then they are non-isomorphic in every forcing extens…
Conjecturesolvedmodel-theory quotient-structures set-theory
0
The forcing-axiom rigidity conjecture for quotients over Borel ideals
arXiv@arxiv
Forcing-axiom rigidity conjecture. CH implies that if there is an isomorphism between
Conjecturesolvedquotient-structures rigidity set-theory
0
The meta-conjecture for Borel quotient structures
arXiv@arxiv
Meta-conjecture. The following statements hold:
Conjecturesolvedquotient-structures rigidity set-theory
2

The conjecture that Martin's Axiom is unnecessary for most quotient lifting results