6 citations · 8 across the 6 of their papers we have counts for
8 papers
The tree property on long intervals of regular cardinals
James Cummings, Yair Hayut, Menachem Magidor +3
In this paper we prove that the tree property can hold on regular cardinals in an interval which overlaps a strong limit cardinal. This is a crucial milestone in the long term proj…
Forcing, genericity and CBERS
Filippo Calderoni, Dima Sinapova
In this paper we continue the study of equivalence of generics filters started by Smythe in [Smy22]. We fully characterize those forcing posets for which the corresponding equivale…
Stationary Reflection and the Failure OF SCH at
Tom Benhamou, Dima Sinapova
Combining stationary reflection (a compactness property) with the failure of SCH (an instance of non-compactness) has been a long-standing theme. We obtain this at ,…
Sigma-Prikry forcing III: Down to Aleph_omega
Alejandro Poveda, Assaf Rinot, Dima Sinapova
We prove the consistency of the failure of the singular cardinals hypothesis at together with the reflection of all stationary subsets of . This shows that…
Sigma-Prikry forcing II: Iteration Scheme
Alejandro Poveda, Assaf Rinot, Dima Sinapova
In Part I of this series, we introduced a class of notions of forcing which we call Sigma-Prikry, and showed that many of the known Prikry-type notions of forcing that center aroun…
Sigma-Prikry forcing I: The Axioms
Alejandro Poveda, Assaf Rinot, Dima Sinapova
We introduce a class of notions of forcing which we call -Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of counta…
The super tree property at the successor of a singular
Sherwood Hachtman, Dima Sinapova
For an inaccessible cardinal , the super tree property (ITP) at holds if and only if is supercomact. However, just like the tree property, it can hold at successor cardi…
Kurepa trees and spectra of -sentences
Dima Sinapova, Ioannis Souldatos
We use set-theoretic tools to make a model-theoretic contribution. In particular, we construct a \emph{single} -sentence that codes Kurepa trees to prove t…