9 citations · 30 across the 23 of their papers we have counts for
24 papers · 1 filter
Universally Baire sets in
Daisuke Ikegami, Matteo Viale
We generalize the basic theory of universally Baire sets of to a theory of universally Baire subsets of . We show that the fundamental characterizations of the property…
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…
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…
Boolean valued semantics for infinitary logics
Juan M. Santiago, Matteo Viale
It is well known that the completeness theorem for fails with respect to Tarski semantics. Mansfield showed that it holds for if one…
Another proof that implies Woodin's axiom
Matteo Viale
Let state that the forcing axiom can be instantiated only for stationary set preserving posets of size at most . We give a detailed acco…
Absolute model companionship, forcibility, and the continuum problem
Matteo Viale
Absolute model companionship (AMC) is a strict strengthening of model companionship defined as follows: For a theory , denotes the logical consequences…