## Paper: Effective domains and intrinsic structure (at LICS 1990)

Authors:**Phoa, W.**

### Abstract

Topos theory is the categorical analog of constructive set theory; and conveniently, PERs (partial equivalence relations) do sit inside a topos-the category of PERs can be (loosely speaking) identified with the full subcategory of modest sets in Hyland's effective topos. (The effective topos is the topos-theoretic version of recursive realizability.) Working in the effective topos is especially attractive since not only can set-theoretic reasoning be used, but one also has a lot of category-theoretic and topos-theoretic machinery at one's disposal. That is the point of view taken in this research. The basic theory of ∑-spaces is discussed. A convex power domain is also presented. Modal operators are outlined. Parallelism and sheaves are examined. Finally, the fixed-point classifier is presented

### BibTeX

@InProceedings{Phoa-Effectivedomainsand, author = {Phoa, W.}, title = {Effective domains and intrinsic structure}, booktitle = {Proceedings of the Fifth Annual IEEE Symp. on Logic in Computer Science, {LICS} 1990}, year = 1990, editor = {John Mitchell}, month = {June}, pages = {366--377}, location = {Philadelphia, PA, USA}, publisher = {IEEE Computer Society Press} }