Constructing illoyal algebra-valued models of set theory
Benedikt Löwe, Robert Paßmann, Sourav Tarafder · Algebra Universalis · 2021
Abstract An algebra-valued model of set theory is calledloyal to its algebraif the model and its algebra have the same propositional logic; it is calledfaithfulif 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: tail stretches, transposition twists, and maximal twists.