caa a22 4500 386385882 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S0305004100001304 doi S0305004100001304 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100001304 A note on inequivalence of realizability toposes [Elektronische Daten] The general construction of realizability toposes was first described in [3]. The data from which such a topos is constructed (called a partial applicative structure in [3]) consists of a set A equipped with a partial binary operation (called application and denoted by juxtaposition, with the convention that unbracketed expressions are evaluated from left to right) and two constants K, S satisfying for all x, y, z A (where, as usual, an equality between possibly undefined terms means ‘one side is defined iff the other is, and then they are equal'). Following Lambek [6], we now call such a structure a partial Schönfinkel algebra, or a global Schönfinkel algebra if application is defined on the whole of A × A. (The name ‘combinatory algebra' is also in common use.) We write for the realizability topos constructed from A. Copyright © Cambridge Philosophical Society 1989 Johnstone P. T. Department of Pure Mathematics, University of Cambridge, Cambridge CB2 1SB Robinson E. P. Department of Computing and Information Science, Queen's University, Kingston, Ont. K7L 3N6, Canada Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 1-3 0305-0041 105:1<1 1989 105 PSP https://doi.org/10.1017/S0305004100001304 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100001304 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Johnstone P. T. Department of Pure Mathematics, University of Cambridge, Cambridge CB2 1SB NATIONALLICENCE 700 1- Robinson E. P. Department of Computing and Information Science, Queen's University, Kingston, Ont. K7L 3N6, Canada NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 1-3 0305-0041 105:1<1 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge