S. Garti

activity

20112021

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13 papers · 1 filter

math.LO2024

Weak diamond and pcf theory

Shimon Garti

We obtain bounds on the cardinality of $p c f (a)$ from instances of weak diamond. Consequently, under mild assumptions there are many singular cardinals of the from $\alep…

math.LO2021

Yablo's paradox and forcing

Shimon Garti

We suggest a forcing version of Yablo's paradox and discuss its implication on self-reference.

math.LO2020

Unbalanced polarized relations

Shimon Garti

We prove the consistency of $(μ μ ^{+}) ↛ (μμ μ ^{+} ω _{1})$ where $μ$ is a strong limit singular cardinal of countable cofinality. This result can be forced at limit…

math.LO2020

Stationary and Closed Rainbow subsets

Shimon Garti, Jing Zhang

We study the structured rainbow Ramsey theory at uncountable cardinals. When compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not…

math.LO2020

Double weakness

Shimon Garti, Saharon Shelah

We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal $λ$ for which the sequence $⟨ 2^{θ} : θ < λ ⟩$ is not eventually constant and the wea…

math.LO2019

Dowker filters and Magidor forcing

Shimon Garti, Yair Hayut

We prove that the consistency of the existence of a Dowker filter at $κ^{+}$ along with $2^{κ} = κ^{+}$ where $κ$ is regular and uncountable. Using Magidor forcing we also prove the consis…