Finite Combinations of Baire Numbers

Details Finite Combinations of Baire Numbers Finite Combinations of Baire Numbers

1992-09-16

arxiv.org/abs/math/9209207v1

Mathematics

Logic

Scientific paper

Let $\kappa$ be a regular cardinal. Consider the Baire numbers of the spaces $(2^{\theta})_\kappa$ (functions from $\theta$ to 2 and the less than $\kappa$ topology) for various $\theta \geq \kappa$. Let l be the number of such different Baire numbers. Models of set theory with l=1 or l=2 are known and it is also known that l is finite. We show here that if $\kappa > \omega$, then l could be any given finite number. We do not know whether the same is true for $\kappa = \omega$.

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