منابع مشابه
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...
متن کاملUniversally Baire Sets and Generic Absoluteness
We prove several equivalences and relative consistency results involving notions of generic absoluteness beyond Woodin’s (Σ ̃ 1)λ generic absoluteness for a limit of Woodin cardinals λ. In particular, we prove that two-step ∃R(Π ̃ 1)λ generic absoluteness below a measurable cardinal that is a limit of Woodin cardinals has high consistency strength, and that it is equivalent with the existence of ...
متن کاملTopological Ramsey spaces and metrically Baire sets
We characterize a class of topological Ramsey spaces such that each element R of the class induces a collection {Rk}k<ω of projected spaces which have the property that every Baire set is Ramsey. Every projected space Rk is a subspace of the corresponding space of length-k approximation sequences with the Tychonoff, equivalently metric, topology. This answers a question of S. Todorcevic and gen...
متن کاملExtending Baire property by uncountably many sets
We prove that if ZFC is consistent so is ZFC + “for any sequence (An) of subsets of a Polish space 〈X, τ〉 there exists a separable metrizable topology τ ′ on X with B(X, τ) ⊆ B(X, τ ′), MGR(X, τ ′) ∩ B(X, τ) = MGR(X, τ) ∩B(X, τ) and An Borel in τ ′ for all n.” This is a category analogue of a theorem of Carlson on the possibility of extending Lebesgue measure to any countable collection of sets...
متن کاملOn Perfect Cones and Absolute Baire-one Retracts
We introduce perfect cones over topological spaces and study their connection with absolute B1-retracts.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1967
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1967-0214031-9