English

A Report on Realizability

Logic 2013-10-01 v3

Abstract

Besides recalling the basic definitions of Realizability Lattices, Abstract Krivine Structures, Ordered Combinatory Algebras and Tripos and reviewing its relationships, we propose a new foundational framework for realizability. Motivated by Streicher's paper "Krivine's Classical Realizability from a Categorical Perspective" [9], we define the concept of Krivine's Ordered Combinatory Algebras (kOKA) as a common platform that is strong enough to do both: categorical and computational semantics. The OCAs produced by Streicher from AKSs in [9] are particular cases of kOKAs.

Keywords

Cite

@article{arxiv.1309.0706,
  title  = {A Report on Realizability},
  author = {Walter Ferrer Santos and Mauricio Guillermo and Octavio Malherbe},
  journal= {arXiv preprint arXiv:1309.0706},
  year   = {2013}
}

Comments

Final report a the project "Classical Realizability, Categories and Games Theory" of ANII-Uruguay

R2 v1 2026-06-22T01:19:47.914Z