Effective compactness and sigma-compactness
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Using the Gandy-Harrington topology and other methods of effective descriptive set theory, we prove several theorems about compact and σ-compact sets. In particular, it is proved that any Δ 1 1 -set A in the Baire space N either is an at most countable union of compact Δ 1 1 -sets (and hence is σ-compact) or contains a relatively closed subset homeomorphic to N (in this case, of course, A cannot be σ-compact).
Keywordseffective descriptive set theory effectively compact σ-compact the Baire space Gandy-Harrington topology Δ11-set
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