Title :
How complete is PER?
Author :
Robinson, Edmund
Author_Institution :
Dept. of Comput. & Inf. Sci., Queen´´s Univ., Kingston, Ont., Canada
Abstract :
The category of partial equivalence relations (PER) on the natural numbers has been used extensively in recent years to model various forms of higher-order type theory. It is known that PER can be viewed as a category of sets in a nonstandard model of intuitionistic Zermelo-Fraenkel set theory. The use of PER as a vehicle for modeling-type theory then arises from completeness properties of this category. The paper demonstrates these completeness properties, and shows that, constructively, some complete categories are more complete than others
Keywords :
equivalence classes; formal logic; number theory; set theory; PER; complete categories; completeness properties; higher-order type theory; intuitionistic Zermelo-Fraenkel set theory; modeling-type theory; natural numbers; nonstandard model; partial equivalence relations; Information science; Set theory; Vehicles;
Conference_Titel :
Logic in Computer Science, 1989. LICS '89, Proceedings., Fourth Annual Symposium on
Conference_Location :
Pacific Grove, CA
Print_ISBN :
0-8186-1954-6
DOI :
10.1109/LICS.1989.39165
