Interpretations of ZF

Published 31 Jan 2024 in math.LO | (2402.00174v1)

Abstract: In this paper, we unify the study of classical and non-classical algebra-valued models of set theory, by studying variations of the interpretation functions for identity and set-membership. Although, these variations coincide with the standard interpretation in Boolean-valued constructions, nonetheless they extend the scope of validity of ZF to new algebra-valued models.

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