We study reflection principles involving nonmeager sets and the Baire Property which are consequences of the generic supercompactness of ω2, such as the principle asserting that any point countable Baire space has a stationary set of closed subspaces of weight ω1 which are also Baire spaces. These principles entail the analogous principles of stationary reflection but are incompatible with forc...

In the article concepts and facts necessary to continue formalization of theory of continuous lattices according to [11] are introduced. and [4] provide the notation and terminology for this paper. 1. PRELIMINARIES The following two propositions are true: (1) For all sets X, A, B such that A ∈ Fin X and B ⊆ A holds B ∈ Fin X. (2) For every set X and for every family F of subsets of X such that ...

In this paper we study the conditions under which a fuzzy topological space becomes a fuzzy almost resolvable space and the inter-relations between fuzzy almost resolvable, fuzzy almost irresolvable spaces, fuzzy submaximal spaces, fuzzy first category spaces, fuzzy Baire spaces, fuzzy weakly Volterra spaces are also investigated.

Metric spaces, Borel and analytic sets, Baire property and measurability, dichotomies, equivalence relations. Possible topics: determinacy, group actions, rigidity, turbulence.