# Synthetic domain theory versus N^\infty-sets

Following Dana Scott’s idea of studying domain-theoretic structures as set-theoretic structures in a model of intuitionistic set theory; especially thinking domains are sets” and continuous maps are maps” and working in a topos, the idea of synthetic domain theory (SDT) formalized in 1991 by Hyland, also Taylor. Then followed and expanded by some other people like Rosolini, Phoa, and Simpson, also few models of synthetic domain theory were introduced (see for example Fiore’s paper).

In this talk, the ideas of Synthetic Domain Theory are considered in the presheaf topos of $\N\infty$-sets, where $\N\infty$ in the monoid of extended natural numbers with the minimum as the binary operation.

This talk is part of the Lab Lunch series.