Fifteenth Annual IEEE Symposium on

Logic in Computer Science (LICS 2000)

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

Authors: L. Birkedal


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.


    author = 	 {L. Birkedal},
    title = 	 {A General Notion of Realizability},
    booktitle =  {Proceedings of the Fifteenth Annual IEEE Symp. on Logic in Computer Science, {LICS} 2000},
    year =	 2000,
    editor =	 {Martin Abadi},
    month =	 {June}, 
    pages =      {7--17},
    location =   {Santa Barbara, CA, USA}, 
    publisher =	 {IEEE Computer Society Press}