Brent Cody

activity

20122021

most citedSome results on large cardinals and the continuum function

6 citations · 6 across the 5 of their papers we have counts for

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8 papers · 1 filter

math.LO2021

Large cardinal ideals

Brent Cody

Building on work of Holy, Lücke and Njegomir \cite{MR3913154} on small embedding characterizations of large cardinals, we use some classical results of Baumgartner (see \cite{MR038…

math.LO2019

A refinement of the Ramsey hierarchy via indescribability

Brent Cody

A subset $S$ of a cardinal $κ$ is Ramsey if for every function $f : [S]^{< ω} \to κ$ with $f (a) < min a$ for all $a \in [S]^{< ω}$ , there is a set $H \subseteq S$ of cardinality $κ$ which i…

math.LO2019

Forcing a $□ (κ)$ -like principle to hold at a weakly compact cardinal

Brent Cody, Victoria Gitman, Chris Lambie-Hanson

Hellsten \cite{MR2026390} proved that when $κ$ is $Π_{n}^{1}$ -indescribable, the \emph{ $n$ -club} subsets of $κ$ provide a filter base for the $Π_{n}^{1}$ -indescribability ideal, and hence…

math.LO2018

Characterizations of the weakly compact ideal on $P_{κ} λ$

Brent Cody

Hellsten \cite{MR2026390} gave a characterization of $Π_{n}^{1}$ -indescribable subsets of a $Π_{n}^{1}$ -indescribable cardinal in terms of a natural filter base: when $κ$ is a $Π_{n}^{1}$ -inde…

math.LO2017

The weakly compact reflection principle need not imply a high order of weak compactness

Brent Cody, Hiroshi Sakai

The weakly compact reflection principle $Refl_{wc} (κ)$ states that $κ$ is a weakly compact cardinal and every weakly compact subset of $κ$ has a weakly compact proper…

math.LO2012★ 6 cited

Some results on large cardinals and the continuum function

Brent Cody

Given a Woodin cardinal $δ$ , I show that if $F$ is any Easton function with $F " δ \subseteq δ$ and $\GCH$ holds, then there is a cofinality-preserving forcing extension in which $2^γ=…

Large cardinal ideals

A refinement of the Ramsey hierarchy via indescribability

Forcing a □(κ)-like principle to hold at a weakly compact cardinal

Characterizations of the weakly compact ideal on Pκ​λ

The weakly compact reflection principle need not imply a high order of weak compactness

Some results on large cardinals and the continuum function

Forcing a $□ (κ)$ -like principle to hold at a weakly compact cardinal

Characterizations of the weakly compact ideal on $P_{κ} λ$