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Logic Seminar

Random graphs: a stronger logic, but with the zero one law , III

Location:  Hill 705
Date & time: Monday, 10 October 2016 at 5:00PM - 5:11PM

Saharon Shelah , The Hebrew University of Jerusalem and Rutgers University: THE TALK CONTINUES.......This is based on paper [1077] We like to find a logic stronger than first order such that: on the one hand it satisfies the 0-1 law, e.g. for the random graph $$cG_{n,1~2}$$ and on the other hand there is a formula $$varphi(x)$$ such that for no first order $$psi(x)$$ do we have: for every random enough $$G_{n,1~2}$$ are the formulas $$varphi(x),psi(x)$$ equivalent in it. We do it adding a quantifier on graph $$bQ_{old t}$$, i.e. have a class of finite graphs closed under isomorphisms and being able to say that if $$(varphi_0(x,ar c),varphi_1(x_0,x_1,ar c))$$ a pair of formulas with parameter define a graph in $$cG_{n,1~2}$$, hen , we can form a formula $$psi(ar y)$$ such $$psi(ar c)$$ says that the graph belongs $$K_{ar{old t}}$$. Presently we do it for random enough $$ar{old t}$$. In later versions we shall do it for $$K_{old t} = {H:H$$ a non-2-weak graph with number of cliques with $$log log(|H|)$$ nodes$$}$$ is one of $$1,2,ldots lfloor sqrt{loglog(|H|)} floor$$ modulo $$lfloor loglog(|H|) floor$$.

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