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Quagmires and large Suslin forests
Lorenzo Notaro
In 1972, Jech asked whether there exists a Suslin -forest in the constructible universe. As reported by Jech, Laver gave a positive answer, but his proof was never publ…
A solution to Ditor's problem
Lorenzo Notaro
We settle the long-standing open question whether there exists a -ladder of cardinality . Given a positive integer , an -ladder is a lower finite lattice whose e…
Open Colorings and Baumgartner's Axiom
Lorenzo Notaro
We construct a model of where Baumgartner's Axiom fails, settling a question of Farah. Moreover, in the same model there is an -de…
Some questions on entangled linear orders
Raphaël Carroy, Maxwell Levine, Lorenzo Notaro
Entangled linear orders were first introduced by Abraham and Shelah. Todorčević showed that these linear orders exist under . We prove the following results: (1) If $\…
Ladders and Squares
Lorenzo Notaro
In 1984, Ditor asked two questions: (1) For each and infinite cardinal , is there a join-semilattice of breadth and cardinality whose principal ideals hav…
Constructibility real degrees in the side-by-side Sacks model
Lorenzo Notaro
We study the join-semilattice of constructibility real degrees in the side-by-side Sacks model, the model of set theory obtained by forcing with a countable-support product of infi…
The breadth of constructibility degrees and definable Sierpiński's coverings
Alessandro Andretta, Lorenzo Notaro
Generalizing a result of Törnquist and Weiss, we study the connection between the existence of Sierpiński's coverings of , and a cardinal invariant of…
Does imply , uniformly?
Alessandro Andretta, Lorenzo Notaro
The Axiom of Dependent Choice and the Axiom of Countable Choice are two weak forms of the Axiom of Choice that can be stated for a specific set: $\mat…
A game for Baire's grand theorem
Lorenzo Notaro
Generalizing a result of Kiss, we provide a game that characterizes Baire class 1 functions between arbitrary separable metrizable spaces. We show that the determinacy of our game…