Implicative algebras: a new foundation for realizability and forcing

20 Feb 2020 Miquel Alexandre

We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this structure is that its elements can be seen both as truth values and as (generalized) realizers, thus blurring the frontier between proofs and types... (read more)

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  • LOGIC