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math.LO2024
Properties preserved by classes of Chu transforms
Francesco Parente
Chu spaces and Chu transforms were first investigated in category theory by Barr and Chu in 1979. In 2000 van Benthem shifted to the model-theoretic point of view by isolating a cl…
math.LO2024
Almost refinement, reaping, and ultrafilter numbers
Jörg Brendle, Michael Hrušák, Francesco Parente
We investigate the combinatorial structure of the set of maximal antichains in a Boolean algebra ordered by almost refinement. We also consider the reaping relation and its associa…
math.LO2024
Generic Absoluteness Revisited
Sakaé Fuchino, Takehiko Gappo, Francesco Parente
The present paper is concerned with the relation between recurrence axioms and Laver-generic large cardinal axioms in light of principles of generic absoluteness and the Ground Axi…