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A note on adding isomorphisms and the pseudointersection number
Corey Bacal Switzer
We prove that for every tower there are -dense and so that any ``reasonable" forcing notion -- an adjective that includes all known ones…
Reflection Properties of Ordinals in Generic Extensions
Juan P. Aguilera, Corey Bacal Switzer
We study the question of when a given countable ordinal is - or -reflecting in models which are neither models nor the constructible universe, focus…
Selective Independence and -Perfect Tree Forcing Notions
Corey Bacal Switzer
Generalizing the proof for Sacks forcing, we show that the -perfect tree forcing notions introduced by Goldstern, Judah and Shelah preserve selective independent families even w…
The Structure of -Maximal Cofinitary Groups
Vera Fischer, Corey Bacal Switzer
We study -maximal cofinitary groups for regular uncountable, . Revisiting earlier work of Kastermans and building upon a recently obtained higher analogue of Bell…
Alternative Cichoń Diagrams and Forcing Axioms Compatible with CH
Corey Bacal Switzer
This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I cons…
Specializing Wide Aronszajn Trees without Adding Reals
Corey Bacal Switzer
We show that under certain circumstances wide Aronszajn trees can be specialized iteratively without adding reals. We then use this fact to study forcing axioms compatible with CH…