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27 papers · 1 filter
Some Results on Finitely Splitting Subtrees of Aronszajn Trees
John Krueger
For any , we introduce a forcing poset using generalized promises which adds a normal -splitting subtree to a -splitting normal Aronszajn tree. Using th…
Intersection Games and Bernstein Sets
James Atchley, Lior Fishman, Saisneha Ghatti
The Banach-Mazur game, Schmidt's game and McMullen's absolute winning game are three quintessential intersection games. We investigate their determinacy on the real line when the t…
A Rigid Kurepa Tree From a Free Suslin Tree
John Krueger
We analyze a countable support product of a free Suslin tree which turns it into a highly rigid Kurepa tree with no Aronszajn subtree. In the process, we introduce a new rigidity p…
Suslin tree preservation and club isomorphisms
John Krueger
We construct a model of set theory in which there exists a Suslin tree and satisfies that any two normal Aronszajn trees, neither of which contains a Suslin subtree, are club isomo…
Sealing from Iterability
Grigor Sargsyan, Nam Trang
We obtain sealing by forcing over a self-iterable model. The proof is fine-structure free and uses only basic ideas from iteration theory. We believe that such fine-structure free…
The exact strength of generic absoluteness for the universally Baire sets
Grigor Sargsyan, Nam Trang
A set of reals is \textit{universally Baire} if all of its continuous preimages in topological spaces have the Baire property. is a type of generic absoluteness cond…