Implicative algebras: a new foundation for realizability and forcing

@article{Miquel2020ImplicativeAA,
  title={Implicative algebras: a new foundation for realizability and forcing},
  author={Alexandre Miquel},
  journal={Mathematical Structures in Computer Science},
  year={2020},
  volume={30},
  pages={458 - 510}
}
  • Alexandre Miquel
  • Published 2020
  • Computer Science, Mathematics
  • Mathematical Structures in Computer Science
Abstract We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model-theoretic 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. We show that each implicative algebra induces a (Set-based) tripos, using a construction that is… Expand
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