|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4661567||1344843||2016||12 صفحه PDF||ندارد||دانلود رایگان|
A construction by Hofmann and Streicher gives an interpretation of a type-theoretic universe U in any Grothendieck topos, assuming a Grothendieck universe in set theory. Voevodsky asked what space U is interpreted as in Johnstone's topological topos. We show that its topological reflection is indiscrete. We also offer a model-independent, intrinsic or synthetic, description of the topology of the universe: It is a theorem of type theory that the universe is sequentially indiscrete, in the sense that any sequence of types converges to any desired type, up to equivalence. As a corollary we derive Rice's Theorem for the universe: it cannot have any non-trivial, decidable, extensional property, unless WLPO, the weak limited principle of omniscience, holds.
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 9, September 2016, Pages 794–805