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math.LO2021
Provability Logic: models within models in Peano Arithmetic
Alessandro Berarducci, Marcello Mamino
In 1994 Jech gave a model theoretic proof of Gödel's second incompleteness theorem for Zermelo-Fraenkel set theory in the following form: ZF does not prove that ZF has a model. Kot…
math.LO2021
Orthogonal decomposition of definable groups
Alessandro Berarducci, Pantelis E. Eleftheriou, Marcello Mamino
Orthogonality in model theory captures the idea of absence of non-trivial interactions between definable sets. We introduce a somewhat opposite notion of cohesiveness, capturing th…