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Abstract  

We show that it is consistent with ZFC that the family of functions with the Baire property has the difference property. That is, every function for which f(x + h)-f(x) has the Baire property for every h∈R is of the form f=g + Awhere g has the Baire property and A is additive.

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Abstract  

We consider Problems 2 and 3 in [3] asked by M. Laczkovich concerning the difference property of Borel measurable functions. We show that the axiom of determinacy implies affirmative answer to Problem 2 (Theorem 2) and that Problem 3 is settled affirmatively for all infinite order Baire classes (Theorem 1.)

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Abstract  

We prove that axiom CPAgame prism, which follows from the Covering Property Axiom CPA and holds in the iterated perfect set model, implies that there exists a Hamel basis which is a union of less than continuum many pairwise disjoint perfect sets. We will also give two consequences of this last fact.

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