The absolute Baire property

Stationary Reflection and the Universal Baire Property

In this note we show that ω1-Universally Baire selfjustifying systems are fully Universally Baire under the Weak Stationary Reflection Principle for Pairs. This involves analyzing the notion of a weakly captured set of reals, a weakening of the Universal Baire property.

Weak difference property of functions with the Baire property

We prove that the class of functions with the Baire property has the weak difference property in category sense. That is, every function for which f(x+h)−f(x) has the Baire property for every h ∈ R can be written in the form f = g+H+φ where g has the Baire property, H is additive, and for every h ∈ R we have φ(x+h)−φ(x) 6= 0 only on a meager set. We also discuss the weak difference property of ...

Baire Property and Axiom of Choice

Extending 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...

The Hurewicz Covering Property and Slaloms in the Baire Space

According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X sa...