8 papers
Second order logic and Set Theory Redux
Jouko Väänänen
We argue that second order logic is a weaker form of set theory, despite the fact that the former is formalized in a second order langauge and the latter in a first order language.…
Inner models from extended logics and the Delta-operation
Jouko Väänänen, Ur Ya'ar
If is an abstract logic (a.k.a. model theoretic logic), we can define the inner model by replacing first order logic with in Gödel's d…
Expressibility and inexpressibility in propositional team logics
Matilda Häggblom, Minna Hirvonen, Jouko Väänänen
We develop dimension theoretic methods for propositional team based logics. Such quantitative methods were defined for team based first-order logic in a recent paper by Hella, Luos…
Aronszajn trees and maximality
Omer Ben-Neria, Siiri Kivimäki, Menachem Magidor +1
Assuming the consistency of a weakly compact cardinal above a regular uncountable cardinal , we prove the consistency of the existence of a wide -Aronszajn tree, i.e. a t…
On Borel subsets of generalized Baire spaces
Tapani Hyttinen, Miguel Moreno, Jouko Väänänen
We develop Descriptive Set Theory in Generalized Baire Spaces without assuming . We point out that without this assumption the basic topological concepts of these spac…
New inner models from second order logics
Menachem Magidor, Jouko Väänänen
We define a new inner model C2(omega) based on the fragment of second order logic in which second order variables range over countable subsets of the domain. We compare C2(omega) t…