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Logic Seminar

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

Location:  Hill 705
Date & time: Monday, 19 September 2016 at 5:00PM - 5:11PM

Saharon Shelah, The Hebrew University of Jerusalem and Rutgers University: '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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Department of Mathematics

Department of Mathematics
Rutgers University
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