Baire space and second category extensions

Baire Category Quantifier in Monadic Second Order Logic

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...

On the Baire Category Theorem

Let T be a topological structure and let A be a subset of the carrier of T . Then IntA is a subset of T . Let T be a topological structure and let P be a subset of the carrier of T . Let us observe that P is closed if and only if: (Def. 1) −P is open. Let T be a non empty topological space and let F be a family of subsets of T . We say that F is dense if and only if: (Def. 2) For every subset X...

Baire Category for Monotone Sets

We study Baire category for downward-closed subsets of 2ω , showing that it behaves better in this context than for general subsets of 2ω . We show that, in the downward-closed context, the ideal of meager sets is prime and b-complete, while the complementary filter is g-complete. We also discuss other cardinal characteristics of this ideal and this filter, and we show that analogous results fo...

The Baire Theory of Category

The Baire theory of category, which classifies sets into two distinct categories, is an important topic in the study of metric spaces. Many results in topology arise from category theory; in particular, the Baire categories are related to a topological property. Because the Baire Category Theorem involves nowhere dense sets in a complete metric space, this paper first develops the concepts of n...

Baire Category, Probabilistic Constructions and Convolution Squares