Paper: A General Notion of Realizability (at LICS 2000)

Authors: Lars Birkedal

Abstract

We present a general notion of realizability encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial Cartesian closed categories. We show how the general notion of realizability can be used to get models of dependent predicate logic, thus obtaining as a corollary (the known result) that the category Equ of equilogical spaces models dependent predicate logic. Moreover, we characterize when the general notion of realizability gives rise to a topos.

BibTeX

  @InProceedings{Birkedal-AGeneralNotionofRea,
    author = 	 {Lars Birkedal},
    title = 	 {A General Notion of Realizability},
    booktitle =  {Proceedings of the Fifteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2000)},
    year =	 {2000},
    month =	 {June}, 
    pages =      {7--17},
    location =   {Santa Barbara, CA, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }