Abstract:
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 Δ11-set A in the Baire space N either is an at most countable union of compact Δ11-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).
Keywords:
effective descriptive set theory, effectively compact, σ-compact, the Baire space, Gandy–Harrington topology, Δ11-set.
Citation:
V. G. Kanovei, V. A. Lyubetskii, “Effective Compactness and Sigma-Compactness”, Mat. Zametki, 91:6 (2012), 840–852; Math. Notes, 91:6 (2012), 789–799
This publication is cited in the following 2 articles:
Lyubetsky V.A. Seliverstov A.V., “A novel algorithm for solution of a combinatory set partitioning problem”, J. Commun. Technol. Electron., 61:6 (2016), 705–708
V. G. Kanovei, V. A. Lyubetskii, “On Effective σ-Boundedness and σ-Compactness in Solovay's Model”, Math. Notes, 98:2 (2015), 273–282