Compact covering mappings between Borel sets and the size of constructible reals
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- by Gabriel Debs and Jean Saint Raymond
- Trans. Amer. Math. Soc. 356 (2004), 73-117
- DOI: https://doi.org/10.1090/S0002-9947-03-03206-9
- Published electronically: August 25, 2003
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Abstract:
We prove that the topological statement: “Any compact covering mapping between two Borel sets is inductively perfect" is equivalent to the set-theoretical statement: $“ \forall \alpha \in \omega ^\omega ,\; \aleph _1^{L(\alpha )}<\aleph _1$".References
- Jens Peter Reus Christensen, Necessary and sufficient conditons for the measurability of certain sets of closed subsets, Math. Ann. 200 (1973), 189–193. MR 334169, DOI 10.1007/BF01425230
- Gabriel Debs and Jean Saint Raymond, Compact covering and game determinacy, Topology Appl. 68 (1996), no. 2, 153–185. MR 1374079, DOI 10.1016/0166-8641(95)00058-5
- Gabriel Debs and Jean Saint Raymond, Cofinal ${\bfSigma }^1_1$ and ${\bfPi }^1_1$ subsets of $\omega ^\omega$, Fund. Math. 159 (1999), no. 2, 161–193. MR 1670079, DOI 10.4064/fm-159-2-161-193
- G. Debs and J. Saint Raymond, Compact covering mappings and cofinal families of compact subsets of a Borel set, Fund. Math. 167 (2001), no. 3, 213–249. MR 1815089, DOI 10.4064/fm167-3-2
- Gabriel Debs and Jean Saint Raymond, Applications semi-propres sur un espace borélien, C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 5, 423–426 (French, with English and French summaries). MR 1826628, DOI 10.1016/S0764-4442(00)01828-0
- Winfried Just and Howard Wicke, Some conditions under which tri-quotient or compact-covering maps are inductively perfect, Topology Appl. 55 (1994), no. 3, 289–305. MR 1259511, DOI 10.1016/0166-8641(94)90043-4
- Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 561709
- A. V. Ostrovskiĭ, On new classes of mappings associated with $k$-covering mappings, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 4 (1994), 24–28, 75 (Russian, with Russian summary); English transl., Moscow Univ. Math. Bull. 49 (1994), no. 4, 20–23 (1995). MR 1317090
- Jean Saint-Raymond, Caractérisation d’espaces polonais. D’après des travaux récents de J. P. R. Christensen et D. Preiss, Séminaire Choquet, 11e–12e années (1971–1973), Initiation à l’analyse, Secrétariat Mathématique, Paris, 1973, pp. Exp. No. 5, 10 (French). MR 0473133
Bibliographic Information
- Gabriel Debs
- Affiliation: Analyse Fonctionnelle, Institut de Mathématique de Jussieu, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France
- MR Author ID: 55795
- Email: gad@ccr.jussieu.fr
- Jean Saint Raymond
- Affiliation: Analyse Fonctionnelle, Institut de Mathématique de Jussieu, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France
- Email: jsr@ccr.jussieu.fr
- Received by editor(s): May 31, 2001
- Published electronically: August 25, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 73-117
- MSC (2000): Primary 03E15; Secondary 03E45, 54H05
- DOI: https://doi.org/10.1090/S0002-9947-03-03206-9
- MathSciNet review: 2020025