We combine some tools from stability theory and finite model theory to prove the following results. Theorem. Let T_∞ be the almost sure theory for a class K and probability P satisfying the first order 0-1 law. Suppose for some K, there are infinitely many distinct L~k-types consistent with T_∞. If LFP logic and first order-logic are almost Everywhere equivalent with respect to P then T_∞ is unstable. Theorem. For appropriate functions f determining The interpretation of the Ramsey quantifier the logic L_ω,ω (Q_r αm, f) is almost every where equivalent to first-order Logic on graphs with respect to edge probability n~-α irrational α.
展开▼
