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arXiv · 1103.1060

On effective compactness and sigma-compactness

Vladimir Kanovei
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Abstract

Using the Gandy -- Harrington topology and other methods of effective descriptive set theory, we prove several theorems on compact and sigma-compact pointsets. In particular we show that any $\Sigma^1_1$ set $A$ of the Baire space $N^N$ either is covered by a countable union of compact $\Delta^1_1$ sets, or $A$ contains a subset closed in $N^N$ and homeomorphic to $N^N$ (and then $A$ is not covered by a sigma-compact set, of course).

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Vladimir Kanovei. 2011-03-05. On effective compactness and sigma-compactness. https://doi.org/10.4213/mzm8544

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