Eventually different functions and inaccessible cardinals

抄録

In this paper, we are considering the Baire property of the eventually different topology as a regularity property for sets of reals and investigate the logical strength of the statements “Every Δ¹₂ set has the Baire property in the eventually different topology” and “Every Σ¹₂ set has the Baire property in the eventually different topology”. The latter statement turns out to be equivalent to “ω₁ is inaccessible by reals”.