Journal of Logic and Computation, Volume 10, Issue 2, pp. 209212: Abstract.
Stability, the finite cover property and 01 lawsJT Baldwin Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, USA, Email: jbaldwin@math.uic.edu
We combine some tools from stability theory and finite model theory to prove the following results. Theorem. Let T_{[infin]} be the almost sure theory for a class K and probability P satisfying the first order 01 law. Suppose for some [kgr], there are infinitely many distinct L^{[kgr]}types consistent with T_{[infin]}. If LFP logic and first orderlogic are almost everywhere equivalent with respect to P and T_{[infin]} is unstable. Theorem. For appropriate functions f determining the interpretation of the Ramsey quantifier the logic L_{[ohgr],[ohgr]}(Q_{ram,f}) is almost everywhere equivalent to firstorder logic on graphs with respect to edge probability n^{[agr]} for irrational [agr]. Keywords: finite model theory, stability theory.
