Curial Gallart

collaborators

3 papers

math.LO2026

Strong failures of club guessing at the successor of a regular cardinal

Curial Gallart

Starting from a model of $ZFC$ , we force the simultaneous failure of the Very Weak Club Guessing and the $℧$ principles at $S_{κ}^{κ^{+}}$ , for any regular cardinal $κ$ . Ou…

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.LO2026

Forcing with Symmetric Systems of Models of Two Types

Curial Gallart

The purpose of this paper is to present a general method for forcing on $I ¨ _{2}$ and $I ¨ _{3}$ with finite conditions, while preserving all cardinals and some fragments of $\mathrm{GCH}…

Strong failures of club guessing at the successor of a regular cardinal

Long Strong Chains of Subsets of I¨1​

Forcing with Symmetric Systems of Models of Two Types

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