12 found
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  1.  14
    Analytic Ideals and Their Applications.Sławomir Solecki - 1999 - Annals of Pure and Applied Logic 99 (1-3):51-72.
    We study the structure of analytic ideals of subsets of the natural numbers. For example, we prove that for an analytic ideal I, either the ideal {X (Ω × Ω: En X ({0, 1,…,n} × Ω } is Rudin-Keisler below I, or I is very simply induced by a lower semicontinuous submeasure. Also, we show that the class of ideals induced in this manner by lsc submeasures coincides with Polishable ideals as well as analytic P-ideals. We study this class of (...)
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  2.  21
    Borel Equivalence Relations and Lascar Strong Types.Krzysztof Krupiński, Anand Pillay & Sławomir Solecki - 2013 - Journal of Mathematical Logic 13 (2):1350008.
    The "space" of Lascar strong types, on some sort and relative to a given complete theory T, is in general not a compact Hausdorff topological space. We have at least three aims in this paper. The first is to show that spaces of Lascar strong types, as well as other related spaces and objects such as the Lascar group Gal L of T, have well-defined Borel cardinalities. The second is to compute the Borel cardinalities of the known examples as well (...)
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  3.  45
    Analytic Ideals.Sławomir Solecki - 1996 - Bulletin of Symbolic Logic 2 (3):339-348.
  4.  23
    Covering Analytic Sets by Families of Closed Sets.Sławomir Solecki - 1994 - Journal of Symbolic Logic 59 (3):1022-1031.
    We prove that for every family I of closed subsets of a Polish space each Σ 1 1 set can be covered by countably many members of I or else contains a nonempty Π 0 2 set which cannot be covered by countably many members of I. We prove an analogous result for κ-Souslin sets and show that if A ♯ exists for any $A \subset \omega^\omega$ , then the above result is true for Σ 1 2 sets. A theorem (...)
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  5.  29
    Actions of Non-Compact and Non-Locally Compact Polish Groups.Sławomir Solecki - 2000 - Journal of Symbolic Logic 65 (4):1881-1894.
    We show that each non-compact Polish group admits a continuous action on a Polish space with non-smooth orbit equivalence relation. We actually construct a free such action. Thus for a Polish group compactness is equivalent to all continuous free actions of this group being smooth. This answers a question of Kechris. We also establish results relating local compactness of the group with its inability to induce orbit equivalence relations not reducible to countable Borel equivalence relations. Generalizing a result of Hjorth, (...)
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  6.  20
    A Gδ Ideal of Compact Sets Strictly Above the Nowhere Dense Ideal in the Tukey Order.Justin Tatch Moore & Sławomir Solecki - 2008 - Annals of Pure and Applied Logic 156 (2):270-273.
    We prove that there is a -ideal of compact sets which is strictly above in the Tukey order. Here is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veličković asked in [Alain Louveau, Boban Veličković, Analytic ideals and cofinal types, Ann. Pure Appl. Logic 99 171–195].
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  7. Vassar College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW]Anuj Dawar Beklemishev, Mirna Dzamonja, David Evans, Erich Grädel, Denis Hirschfeldt, Hannes Leitgeb, Roger Maddux, Grigori Mints, Volker Peckhaus & Sławomir Solecki - 2008 - Bulletin of Symbolic Logic 14 (4).
     
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  8.  26
    Vassar College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW]David M. Evans, Erich Grädel, Geoffrey P. Hellman, Denis Hirschfeldt, Thomas J. Jech, Julia Knight, Michael C. Laskowski, Volker Peckhaus, Wolfram Pohlers & Sławomir Solecki - 2005 - Bulletin of Symbolic Logic 11 (1):37.
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  9. Tukey Order Among F Σ Ideals.Jialiang He, Michael Hrušák, Diego Rojas-Rebolledo & Sławomir Solecki - forthcoming - Journal of Symbolic Logic:1-15.
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  10.  15
    Coherent Extension of Partial Automorphisms, Free Amalgamation and Automorphism Groups.Daoud Siniora & Sławomir Solecki - 2020 - Journal of Symbolic Logic 85 (1):199-223.
    We give strengthened versions of the Herwig–Lascar and Hodkinson–Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous structures. For instance, we establish a coherent form of the extension property for partial automorphisms for certain Fraïssé classes. We deduce from these results that the isometry group of the rational Urysohn space, the automorphism group of the Fraïssé limit of any Fraïssé class that is the class of all ${\cal F}$-free structures, and (...)
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  11.  19
    Greg Hjorth and Alexander S. Kechris. Analytic Equivalence Relations and Ulm-Type Classifications. The Journal of Symbolic Logic, Vol. 60 , Pp. 1273–1300. - Greg Hjorth, Alexander S. Kechris, and Alain Louveau. Borel Equivalence Relations Induced by Actions of the Symmetric Group. Annals of Pure and Applied Logic, Vol. 92 , Pp. 63–112. [REVIEW]Sławomir Solecki - 2001 - Bulletin of Symbolic Logic 7 (4):541-544.
  12.  4
    The Journal of Symbolic Logic.Sławomir Solecki - 2001 - Bulletin of Symbolic Logic 7 (4):541-544.