Geodesic
Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$
Fundamenta Mathematicae, Tome 159 (1999) no. 2, pp. 161-193.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 ≤*".
DOI : 10.4064/fm-159-2-161-193

Gabriel Debs 1 ; Jean Saint Raymond 1

1 
@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. http://geodesic.mathdoc.fr/articles/10.4064/fm-159-2-161-193/

Cité par Sources :