תואר : מגיסטר

מנחה : פרופ"ח רון רוזנטל

כותרת

Generalization of Shelah and Spencer 0-1 Laws to Multi - Parameter Random Simplicial Complexes

אבסטרקט

The Erdős-Rényi model G(n, p), is a random graph on n vertices, where each edge is added independently with probability p = p(n). Zero-one laws for random graphs and in particular for G(n, p) have been extensively studied since the appearance of random graph models. In particular, two striking results regarding the behaviour of first-order logic properties in the Erdős-Rényi model are: 1. In 1969 Glebski˘ı, Kogan, Liogon’ki˘ı, Talanov and independently in 1976 Fagin proved that for p which is independent of n (fixed), every first order logic property of G(n, p) is either true asymptotically almost surely or false asymptotically almost surely. 2. In 1988 Shelah and Spencer extended the above zero-one law into the case where p = n−α for any irrational α. In this talk we will discuss generalizations of such zero-one laws to random simplicial complexes of arbitrary dimension and show that analogue statements hold.78/87 The talk is based on my master thesis under the supervision of 14on Rosenthal