9 citations · 30 across the 23 of their papers we have counts for
5 papers · 2 filters
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…
The model-companionship spectrum of set theory, generic absoluteness, and the Continuum problem
Matteo Viale
We show that for -properties of second or third order arithmetic as formalized in appropriate natural signatures the apparently weaker notion of forcibility overlaps with the…
Incompatible bounded category forcing axioms
David Aspero, Matteo Viale
We introduce bounded category forcing axioms for well-behaved classes . These are strong forms of bounded forcing axioms which completely decide the theory of some initial segme…