6 problems

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Equiconsistency of the nonexistence of infinite mad families with ZF
Let $\mathfrak F$ be the class of ideals on $\operatorname{\mathbb{N}}$ described above, and consider the theory obtained by adjoining to ${\mathsf{ZF}}$ the assertion that there a…
Conjectureopenconsistency-strength mad-families set-theoryarXiv posted 2 days ago
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Proper destruction conjecture for MAD families
Proper destruction conjecture for MAD families. Every MAD family can be destroyed by a proper forcing that does not add dominating or unsplit reals.
Conjectureopencardinal-invariants mad-families set-theoretic-forcingarXiv posted 2 days ago
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The diamond principle conjecture for mad families of block subspaces
Let $F$ be a countable field, and let $\diamondsuit(\omega^\omega,=^\infty)$ denote the parameterized diamond principle appearing in the source. Diamond principle conjecture. If…
Conjectureopencardinal-invariants mad-families set-theoryarXiv posted 2 days ago
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The cardinal-invariant lower-bound conjecture for mad families of subspaces
Let $F$ be a countable field, let $mathrm{non}(mathcal{M})$ denote the uniformity of the meager ideal, and let $mathfrak{a}{mathrm{vec},F}$ be the least cardinality of a mad famil…
Conjectureopencardinal-invariants mad-families set-theoryarXiv posted 2 days ago
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Existence of Sacks-indestructible MAD families below ${\aleph}_{\omega}$
Sacks-indestructibility conjecture. If
Conjectureopencardinal-invariants mad-families set-theoryarXiv posted 2 days ago
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Nonexistence of weakly tight families at ${\aleph}_1<\mathfrak{s}=\mathfrak{c}=\aleph_2$
Nonexistence conjecture. There is a model of
Conjectureopencardinal-invariants mad-families set-theoryarXiv posted 2 days ago

6 problems

Equiconsistency of the nonexistence of infinite mad families with ZF

Proper destruction conjecture for MAD families

The diamond principle conjecture for mad families of block subspaces

The cardinal-invariant lower-bound conjecture for mad families of subspaces

Existence of Sacks-indestructible MAD families below ℵω{\aleph}_{\omega}ℵω​

Nonexistence of weakly tight families at ℵ1<s=c=ℵ2{\aleph}_1<\mathfrak{s}=\mathfrak{c}=\aleph_2ℵ1​<s=c=ℵ2​

Existence of Sacks-indestructible MAD families below ${\aleph}_{\omega}$

Nonexistence of weakly tight families at ${\aleph}_1<\mathfrak{s}=\mathfrak{c}=\aleph_2$