10 found
  1.  13
    Borel equivalence relations induced by actions of the symmetric group.Greg Hjorth, Alexander S. Kechris & Alain Louveau - 1998 - Annals of Pure and Applied Logic 92 (1):63-112.
    We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially Π03 iff the invariants are countable sets of reals, it is potentially Π04 iff the invariants are countable sets of countable sets of reals, and so on. The proofs (...)
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  2.  19
    Analytic ideals and cofinal types.Alain Louveau & Boban Velickovi - 1999 - Annals of Pure and Applied Logic 99 (1-3):171-195.
  3.  47
    On the quasi-ordering of borel linear orders under embeddability.Alain Louveau & Jean Saint-Raymond - 1990 - Journal of Symbolic Logic 55 (2):537-560.
    We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in R ω , with the lexicographic ordering. For Borel orders embeddable in R 2 , our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some $\mathbf{R}^n, n , and hyperprojective determinacy for the general case.
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  4.  21
    Two results on borel orders.Alain Louveau - 1989 - Journal of Symbolic Logic 54 (3):865-874.
    We prove two results about the embeddability relation between Borel linear orders: For $\eta$ a countable ordinal, let $2^\eta$ (resp. $2^{<\eta}$) be the set of sequences of zeros and ones of length $\eta$ (resp. $<\eta$), equipped with the lexicographic ordering. Given a Borel linear order $X$ and a countable ordinal $\xi$, we prove the following two facts. (a) Either $X$ can be embedded (in a $\triangle^1_1(X,\xi)$ way) in $2^{\omega\xi}$, or $2^{\omega\xi + 1}$ continuously embeds in $X$. (b) Either $X$ can (...)
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  5.  6
    Descriptive Set Theory and Harmonic Analysis.Howard S. Becker, R. Dougherty, A. S. Kechris, Alexander S. Kechris, Alain Louveau & A. Louveau - 2002 - Bulletin of Symbolic Logic 8 (1):94.
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  6.  30
    San Antonio Convention Center San Antonio, Texas January 14–15, 2006.Douglas Cenzer, C. Ward Henson, Michael C. Laskowski, Alain Louveau, Russell Miller, Itay Neeman, Sergei Starchenko & Valentina Harizanov - 2006 - Bulletin of Symbolic Logic 12 (4).
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  7.  7
    [Omnibus Review].Alain Louveau - 1987 - Journal of Symbolic Logic 52 (3):869-870.
  8.  4
    Recursivity and capacity theory.Alain Louveau - 1985 - In Anil Nerode & Richard A. Shore (eds.), Recursion theory. Providence, R.I.: American Mathematical Society. pp. 285--301.
  9.  69
    Jack H. Silver. Counting the number of equivalence classes of Borel and coanalytic equivalence relations. Annals of mathematical logic, vol. 18 , pp. 1–28. - John P. Burgess. Equivalences generated by families of Borel sets. Proceedings of the American Mathematical Society. vol. 69 , pp. 323–326. - John P. Burgess. A reflection phenomenon in descriptive set theory. Fundamenta mathematicae. vol. 104 , pp. 127–139. - L. Harrington and R. Sami. Equivalence relations, projective and beyond. Logic Colloquium '78, Proceedings of the Colloquium held in Mons, August 1978, edited by Maurice Boffa, Dirk van Dalen, and Kenneth McAloon, Studies in logic and the foundations of mathematics, vol. 97, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1979, pp. 247–264. - Leo Harrington and Saharon Shelah. Counting equivalence classes for co-κ-Souslin equivalence relations. Logic Colloquium '80, Papers intended for the European summer meeting of the Association for Symbolic Logic, edit. [REVIEW]Alain Louveau - 1987 - Journal of Symbolic Logic 52 (3):869-870.
  10.  28
    Counting the Number of Equivalence Classes of Borel and Coanalytic Equivalence Relations.Equivalences Generated by Families of Borel Sets.A Reflection Phenomenon in Descriptive Set Theory.Equivalence Relations, Projective and Beyond.Counting Equivalence Classes for co-κ-Souslin Equivalence Relations.On Lusin's Restricted Continuum Problem. [REVIEW]Alain Louveau - 1987 - Journal of Symbolic Logic 52 (3):869-870.