Monroe Eskew

activity

20182021

collaborators

10 papers

math.LO2021

Strong independence and its spectrum

Monroe Eskew, Vera Fischer

For $μ, κ$ infinite, say $A \subseteq [κ]^{κ}$ is a $(μ, κ)$ -maximal independent family if whenever $A_{0}$ and $A_{1}$ are pairwise disjoint non-empty in $[\…

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.LO2019

On a strengthening of Jónssonness for $ℵ_{ω}$

Monroe Eskew

We discuss a system of strengthenings of " $ℵ_{ω}$ is Jónsson" indexed by real numbers, and identify a strongest one. We give a proof of a theorem of Silver and show that there i…

math.LO2019

More rigid ideals

Monroe Eskew

We extend prior results of Cody-Eskew, showing the consistency of GCH with the statement that for all regular cardinals $κ \leq λ$ , where $κ$ is the successor of a regular cardinal,…

math.LO2019

Generic large cardinals as axioms

Monroe Eskew

We argue against Foreman's proposal to settle the continuum hypothesis and other classical independent questions via the adoption of generic large cardinal axioms.

math.LO2019

Some mutually inconsistent generic large cardinals

Monroe Eskew

Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.

Strong independence and its spectrum

Compactness versus hugeness at successor cardinals

On a strengthening of Jónssonness for ℵω​

More rigid ideals

Generic large cardinals as axioms

Some mutually inconsistent generic large cardinals

On a strengthening of Jónssonness for $ℵ_{ω}$