19 found
Order:
Disambiguations
Sławomir Solecki [13]Slawomir Solecki [5]S. Solecki [2]Slawomir J. Solecki [1]
  1.  27
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   34 citations  
  2.  70
    Analytic ideals.Sławomir Solecki - 1996 - Bulletin of Symbolic Logic 2 (3):339-348.
    §1. Introduction. Ideals and filters of subsets of natural numbers have been studied by set theorists and topologists for a long time. There is a vast literature concerning various kinds of ultrafilters. There is also a substantial interest in nicely definable ideals—these by old results of Sierpiński are very far from being maximal— and the structure of such ideals will concern us in this announcement. In addition to being interesting in their own right, Borel and analytic ideals occur naturally in (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  3.  37
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  4.  13
    Tukey order among ideals.Jialiang He, Michael Hrušák, Diego Rojas-Rebolledo & Sławomir Solecki - 2021 - Journal of Symbolic Logic 86 (2):855-870.
    We investigate the Tukey order in the class of Fσ ideals of subsets of ω. We show that no nontrivial Fσ ideal is Tukey below a Gδ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, we (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  5.  20
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  49
    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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  7.  40
    Dominating and unbounded free sets.Slawomir Solecki & Otmar Spinas - 1999 - Journal of Symbolic Logic 64 (1):75-80.
    We prove that every analytic set in ω ω × ω ω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set, and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  8. Decomposing baire functions.J. Cichoń, M. Morayne, J. Pawlikowski & S. Solecki - 1991 - Journal of Symbolic Logic 56 (4):1273 - 1283.
    We discuss in the paper the following problem: Given a function in a given Baire class, into "how many" (in terms of cardinal numbers) functions of lower classes can it be decomposed? The decomposition is understood here in the sense of the set-theoretical union.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  9.  34
    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].
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  10.  48
    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, (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  11.  34
    1995–1996 annual meeting of the association for symbolic logic.Tomek Bartoszynski, Harvey Friedman, Geoffrey Hellman, Bakhadyr Khoussainov, Phokion G. Kolaitis, Richard Shore, Charles Steinhorn, Mirna Dzamonja, Itay Neeman & Slawomir Solecki - 1996 - Bulletin of Symbolic Logic 2 (4):448-472.
  12.  30
    Moscone Center West, San Francisco, CA January 15–16, 2010.Fernando J. Ferreira, John Harrison, François Loeser, Chris Miller, Joseph S. Miller, Slawomir J. Solecki, Stevo Todorcevic & John Steel - 2010 - Bulletin of Symbolic Logic 16 (3).
    Direct download  
     
    Export citation  
     
    Bookmark  
  13.  20
    Phoenix Civic Plaza, Phoenix, Arizona, January 9–10, 2004.Matthew Foreman, Steve Jackson, Julia Knight, R. W. Knight, Steffen Lempp, Françoise Point, Kobi Peterzil, Leonard Schulman, Slawomir Solecki & Carol Wood - 2004 - Bulletin of Symbolic Logic 10 (2).
    Direct download  
     
    Export citation  
     
    Bookmark  
  14.  35
    Trichotomies for Ideals of Compact Sets.É Matheron, S. Solecki & M. Zelený - 2006 - Journal of Symbolic Logic 71 (2):586 - 598.
    We prove several trichotomy results for ideals of compact sets. Typically, we show that a "sufficiently rich" universally Baire ideal is either $\Pi _{3}^{0}$-hard, or $\Sigma _{3}^{0}$-hard, or else a σ-ideal.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  15. 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).
     
    Export citation  
     
    Bookmark  
  16.  36
    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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  17.  18
    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.
  18.  10
    Review: Greg Hjorth, Alexander S. Kechris, Analytic Equivalence Relations and Ulm-Type Classifications; Greg Hjorth, Alexander S. Kechris, Alain Louveau, Borel Equivalence Relations Induced by Actions of the Symmetric Group. [REVIEW]Sławomir Solecki - 2001 - Bulletin of Symbolic Logic 7 (4):541-544.
  19.  6
    The Journal of Symbolic Logic. [REVIEW]Sławomir Solecki - 2001 - Bulletin of Symbolic Logic 7 (4):541-544.