Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$

• Autorzy: Gabriel Debs , Jean Saint Raymond
• Języki publikacji: EN

Abstrakty

EN

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 ≤*".

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 03E45: Inner models, including constructibility, ordinal definability, and core models

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 159
• Numer: 2
• Strony: 161-193

Daty

wydano

1999

otrzymano

1998-05-20

Twórcy

autor

Gabriel Debs

autor

Jean Saint Raymond

Bibliografia

• [1] J. Brendle, G. Hjorth and O. Spinas, Regularity properties for dominating projective sets, Ann. Pure Appl. Logic 72 (1995), 291-307.
• [2] J. P. R. Christensen, Necessary and sufficient conditions for the measurability of certain sets of closed sets, Math. Ann. 200 (1973), 189-193.
• [3] G. Debs and J. Saint Raymond, Compact covering and game determinacy, Topology Appl. 68 (1996), 153-185.
• [4] W. Just and H. Wicke, Some conditions under which tri-quotient or compact-covering maps are inductively perfect, ibid. 55 (1994), 289-305.
• [5] A. Louveau, A separation theorem for $∑^1_1$ sets, Trans. Amer. Math. Soc. 260 (1980), 363-378.
• [6] Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam, 1980.
• [7] A. V. Ostrovskiĭ, On new classes of mappings associated with k-covering mappings, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1994, no. 4, 24-28 (in Russian); English transl.: Moscow Univ. Math. Bull. 49 (1994), no. 4, 29-23.
• [8] J. Saint Raymond, Caractérisation d'espaces polonais d'après des travaux récents de J. P. R. Christensen et D. Preiss, Sém. Choquet, 11$^e$-12$^e$ années, Initiation à l'Analyse, exp. no. 5, Secrétariat Mathématique, Paris, 1973, 10 pp.
• [9] J. Saint Raymond, La structure borélienne d'Effros est-elle standard?, Fund. Math. 100 (1979), 201-210.
• [10] O. Spinas, Dominating projective sets in the Baire space, Ann. Pure Appl. Logic 68 (1995), 327-342.