Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$
Fundamenta Mathematicae, Tome 159 (1999) no. 2, pp. 161-193
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We study properties of $∑^1_1$ and $π^1_1$ subsets of $ω^ω$ that are cofinal relative to the orders ≤ (≤*) of full (eventual) domination. We apply these results to prove that the topological statement "Any compact covering mapping from a Borel space onto a Polish space is inductively perfect" is equivalent to the statement "$∀α ∈ω^ω, ω^ω ∩ L(α )$ is bounded for ≤*".
@article{10_4064_fm_159_2_161_193,
author = {Gabriel Debs and Jean Saint Raymond},
title = {Cofinal $\ensuremath{\Sigma}^1_1$ and $\ensuremath{\Pi}^1_1$ subsets of $\ensuremath{\omega}^\ensuremath{\omega}$},
journal = {Fundamenta Mathematicae},
pages = {161--193},
publisher = {mathdoc},
volume = {159},
number = {2},
year = {1999},
doi = {10.4064/fm-159-2-161-193},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-159-2-161-193/}
}
TY - JOUR AU - Gabriel Debs AU - Jean Saint Raymond TI - Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$ JO - Fundamenta Mathematicae PY - 1999 SP - 161 EP - 193 VL - 159 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-159-2-161-193/ DO - 10.4064/fm-159-2-161-193 LA - en ID - 10_4064_fm_159_2_161_193 ER -
%0 Journal Article %A Gabriel Debs %A Jean Saint Raymond %T Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$ %J Fundamenta Mathematicae %D 1999 %P 161-193 %V 159 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/fm-159-2-161-193/ %R 10.4064/fm-159-2-161-193 %G en %F 10_4064_fm_159_2_161_193
Gabriel Debs; Jean Saint Raymond. Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$. Fundamenta Mathematicae, Tome 159 (1999) no. 2, pp. 161-193. doi: 10.4064/fm-159-2-161-193
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