4 papers
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…
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…
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…
Universality properties of forcing
Francesco Parente, Matteo Viale
The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that an…