David Asper'o

activity

20242026

collaborators

3 papers

math.LO2026

Long Strong Chains of Subsets of $I ¨ _{1}$

David AsperÃ³, Curial Gallart

We force the existence of a chain of length $I ¨ _{3}$ in $[I ¨ _{1}]^{I ¨ _{1}}$ increasing modulo finite. The construction involves symmetric systems of models of two types as side condition…

math.LO2025

The proper forcing axiom for $ℵ_{1}$ -sized posets, $I ¨ _{1}$ -linked symmetrically proper forcing, and the size of the continuum

David AsperÃ³, Mohammad Golshani

We show that the Proper Forcing Axiom for forcing notions of size $ℵ_{1}$ is consistent with the continuum being arbitrarily large. In fact, assuming $GC H$ holds and $Îº\geqÏ_2…

math.LO2024

The special Aronszajn tree property at $ℵ_{2}$ and $GC H$

David AsperÃ³, Mohammad Golshani

Starting from the existence of a weakly compact cardinal, we build a generic extension of the universe in which $GC H$ holds and all $ℵ_{2}$ -Aronszajn trees are special and hence…

Long Strong Chains of Subsets of I¨1​

The proper forcing axiom for ℵ1​-sized posets, I¨1​-linked symmetrically proper forcing, and the size of the continuum

The special Aronszajn tree property at ℵ2​ and GCH

Long Strong Chains of Subsets of $I ¨ _{1}$

The proper forcing axiom for $ℵ_{1}$ -sized posets, $I ¨ _{1}$ -linked symmetrically proper forcing, and the size of the continuum

The special Aronszajn tree property at $ℵ_{2}$ and $GC H$