Constructing illoyal algebra-valued models of set theory
Benedikt Löwe, Robert Passmann, Sourav Tarafder
Abstract:
An algebra-valued model of set theory is called loyal to its algebra if the model and its algebra have the same propositional logic; it is called faithful if all elements of the algebra are truth values of a sentence of the language of set theory in the model. We observe that non-trivial automorphisms of the algebra result in models that are not faithful and apply this to construct three classes of illoyal models: the tail stretches, the transposition twists, and the maximal twists.