Sean D. Cox

activity

20182021

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7 papers · 1 filter

math.LO2021

The Diagonal Strong Reflection Principle and its fragments

Sean Cox, Gunter Fuchs

A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the r…

math.LO2020

Compactness versus hugeness at successor cardinals

Sean Cox, Monroe Eskew

If $κ$ is regular and $2^{< κ} \leq κ^{+}$ , then the existence of a weakly presaturated ideal on $κ^{+}$ implies $□_{κ}^{*}$ . This partially answers a question of Foreman and Magidor ab…

math.LO2020

The $Π_{1}^{1} ↓$ Löwenheim-Skolem-Tarski property of Stationary Logic

Sean Cox

Fuchino-Maschio-Sakai~\cite{FuchinoEtAl_DRP_LST} proved that the Löwenheim-Skolem-Tarski (LST) property of Stationary Logic is equivalent to the Diagonal Reflection Principle on in…

math.LO2019

Adjoining only the things you want: a survey of Strong Chang's Conjecture and related topics

Sean Cox

We survey some old and new results on strong variants of Chang's Conjecture and related topics.

math.LO2019

Martin's Maximum and the Diagonal Reflection Principle

Sean Cox, Hiroshi Sakai

We prove that Martin's Maximum does not imply the Diagonal Reflection Principle for stationary subsets of $[ω_{2}]^{ω}$ .

math.LO2018

A variant of Shelah's characterization of Strong Chang's Conjecture