19 citations · 38 across the 6 of their papers we have counts for
7 papers · 1 filter
What model companionship can say about the Continuum problem
Giorgio Venturi, Matteo Viale
We present recent results on the model companions of set theory, placing them in the context of the current debate in the philosophy of mathematics. We start by describing the depe…
The model companions of set theory
Giorgio Venturi, Matteo Viale
This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companions…
Infinite forcing and the generic multiverse
Giorgio Venturi
In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the…
Reflexive insensitive modal logics
David Gilbert, Giorgio Venturi
We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which the…
Preservation of a Souslin tree and side conditions
Giorgio Venturi
We show how to force, with finite conditions, the forcing axiom PFA(T), a relativization of PFA to proper forcing notions preserving a given Souslin tree T. The proof uses a Neeman…
Proper forcing remastered
Boban Velickovic, Giorgio Venturi
In these notes we present the method introduced by Neeman of generalized side conditions with two types of models. We then discuss some applications: the Friedman-Mitchell poset fo…
A direct proof of the five element basis theorem
Boban Velickovic, Giorgio Venturi
We present a direct proof of the consistency of the existence of a five element basis for the uncountable linear orders. Our argument is based on the approach of notion of saturati…