[-- Attachment #1: Type: text/plain, Size: 1548 bytes --] From type theory to setoids and back Erik Palmgren<https://arxiv.org/search/math?searchtype=author&query=Palmgren%2C+E> (Submitted on 3 Sep 2019) A model of Martin-Löf extensional type theory with universes is formalized in Agda, an interactive proof system based on Martin-Löf intensional type theory. This may be understood, we claim, as a solution to the old problem of modelling the full extensional theory in the intensional theory. Types are interpreted as setoids, and the model is therefore a setoid model. We solve the problem of intepreting type universes by utilizing Aczel's type of iterative sets, and show how it can be made into a setoid of small setoids containing the necessary setoid constructions. In addition we interpret the bracket types of Awodey and Bauer. Further quotient types should be interpretable. Comments: 30 pages Subjects: Logic (math.LO) MSC classes: 03B15, 03B35, 03E70, 03F50 Cite as: arXiv:1909.01414<https://arxiv.org/abs/1909.01414> [math.LO] (or arXiv:1909.01414v1<https://arxiv.org/abs/1909.01414v1> [math.LO] for this version) https://arxiv.org/abs/1909.01414 -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/6AC5AAA7-297B-4644-A116-4182A0FC935E%40math.su.se. [-- Attachment #2: Type: text/html, Size: 4852 bytes --]