We prove a model theoretic Baire category theorem for τ̃ f low-sets in a countable simple theory in which the extension property is firstorder and show some of its applications. We also prove a trichotomy for minimal types in countable nfcp theories: either every type that is internal in a minimal type is essentially-1-based by means of the forking topology or T interprets a strongly-minimal for...

We give topological proofs of Görnemann’s adaptation to Heyting algebras of the Rasiowa-Sikorski Lemma for Boolean algebras; and of the Rauszer-Sabalski generalisation of it to distributive lattices. The arguments use the Priestley topology on the set of prime filters, and the Baire category theorem. This is preceded by a discussion of criteria for compactness of various spaces of subsets of a ...

We consider Rabin’s Monadic Second Order logic (MSO) of the full binary tree extended with Harvey Friedman’s “for almost all” second-order quantifier (∀∗) with semantics given in terms of Baire Category. In Theorem 1 we prove that the new quantifier can be eliminated (MSO+∀∗ =MSO). We then apply this result to prove in Theorem 2 that the finite–SAT problem for the qualitative fragment of the pr...

In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon's bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the...

In this paper the Bagley-Torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. The results reveal that the present method is very effective and accurate.

An extension of a topological zero-one law due to M. and K.P.S. Bhaskara Rao and of the Hewitt-Savage zero-one law is presented. In [8] M. and K.P.S. Bhaskara Rao proved the following topological zeroone law, which we shall refer to as the Bhaskara Rao zero-one law. Theorem 1. Let X be a topological space and let $ be a group of homeomorphisms of X onto itself with the property that for any two...

We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. Theorem. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. Theorem. In the Ellentuck topology on [ω] , (s)0 is a proper subset of the...

We present several recent examples of the generic approach to nonlinear problems. In this approach, instead of considering, for instance, the convergence of an algorithm, one investigates an appropriate space of algorithms equipped with some natural complete metric and shows that convergence does indeed occur for most algorithms there. As we shall see, sometimes one can show that the complement...