2 citations · 3 across the 8 of their papers we have counts for
8 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…
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…
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…
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…
Orderings of ultrafilters on Boolean algebras
Jörg Brendle, Francesco Parente
We study two generalizations of the Rudin-Keisler ordering to ultrafilters on complete Boolean algebras. To highlight the difference between them, we develop new techniques to cons…
Combinatorics of ultrafilters on Cohen and random algebras
Jörg Brendle, Francesco Parente
We investigate the structure of ultrafilters on Boolean algebras in the framework of Tukey reducibility. In particular, this paper provides several techniques to construct ultrafil…
Keisler's order via Boolean ultrapowers
Francesco Parente
In this paper, we provide a new characterization of Keisler's order in terms of saturation of Boolean ultrapowers. To do so, we apply and expand the framework of 'separation of var…
On regular ultrafilters, Boolean ultrapowers, and Keisler's order
Francesco Parente
In this paper we analyse and compare two different notions of regularity for filters on complete Boolean algebras. We also announce two results from a forthcoming paper in preparat…