C. Switzer

collaborators

7 papers

math.LO2025

Baumgartner's Axiom and Small Posets

Pedro Marun, Saharon Shelah, Corey Bacal Switzer

We contribute to the study of $ℵ_{1}$ -dense sets of reals, a mainstay in set theoretic research since Baumgartner's seminal work in the 70s. In particular, we show that it is co…

math.LO2025

Adding $ℵ_{I ¨} $ many Cohen reals

Pedro Marun, Saharon Shelah, Corey Bacal Switzer

Abstractly, the generic extensions after $ℵ_{I ¨} $ -many Cohen reals and $ℵ_{I ¨ + 1}$ -many Cohen reals must be different for reasons of uniform density the relevant Boolean alg…

math.LO2025

Eventual Capture on a Measurable Cardinal

Tom Benhamou, Corey Bacal Switzer

We continue the study from \cite{BrendleFreidmanMontoya, vandervlugtlocalizationcardinals} of localization cardinals $\mfb_Îº(\in^*)$ and $\mfd_Îº(\in^*)$ and their variants at reg…

math.LO2025

A note on adding isomorphisms and the pseudointersection number

Corey Bacal Switzer

We prove that for every tower $T$ there are $ℵ_{1}$ -dense $A$ and $B$ so that any ``reasonable" forcing notion $P$ -- an adjective that includes all known ones…

math.LO2025

Variants of Baumgartner's Axiom for Lipschitz Functions on Baire and Cantor Space

Corey Bacal Switzer

We consider several variants of Baumgartner's axiom for $ℵ_{1}$ -dense sets defined on the Baire and Cantor spaces in terms of Lipschitz functions with respect to the usual metri…

math.LO2025

Weak Baumgartner axioms and universal spaces

Corey Bacal Switzer

If $X$ is a topological space and $I^º$ is a cardinal then $BA_{I^} º (X)$ is the statement that for each pair $A, B \subseteq X$ of $I^º$ -dense subsets there is an autohomeomorp…

Baumgartner's Axiom and Small Posets

Adding ℵI¨​ many Cohen reals

Eventual Capture on a Measurable Cardinal

A note on adding isomorphisms and the pseudointersection number

Variants of Baumgartner's Axiom for Lipschitz Functions on Baire and Cantor Space

Weak Baumgartner axioms and universal spaces

Adding $ℵ_{I ¨} $ many Cohen reals