ﻻ يوجد ملخص باللغة العربية
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure theoretic sense. In particular, it gives a new perspective on Vershiks theorems on genericity and randomness of Urysohns space among separable metric spaces.
We first show that in the function realizability topos every metric space is separable, and every object with decidable equality is countable. More generally, working with synthetic topology, every $T_0$-space is separable and every discrete space is
In this paper, we investigate connections between structures present in every generic extension of the universe $V$ and computability theory. We introduce the notion of {em generic Muchnik reducibility} that can be used to to compare the complexity o
We prove a strong non-structure theorem for a class of metric structures with an unstable pair of formulae. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies severa
The general theory developed by Ben Yaacov for metric structures provides Fraisse limits which are approximately ultrahomogeneous. We show here that this result can be strengthened in the case of relational metric structures. We give an extra conditi
We prove that a wide Morley sequence in a wide generically stable type is isometric to the standard basis of an $ell_p$ space for some $p$.