Induced Cylindric Algebras of Choice Structures

Abstract

One of the benefit properties implied by the extensionality axiom of Hilbert's epsilon calculus is that the calculus becomes complete with respect to the choice structures as semantics. Another implication of the axiom, discussed in the paper, is that an algebra is induced over the universe of the canonical model of a theory, which is isomorphic to a quotient algebra of the Lindenbaum--Tarski algebra of the theory. Especially, in the case of Boolean or monadic algebras, the canonical model of the theory of a sigma complete model is isomorphic to the algebra induced by the axiom of extensionality.