29 found
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  1.  9
    Borel Equivalence Relations and Classifications of Countable Models.Greg Hjorth & Alexander S. Kechris - 1996 - Annals of Pure and Applied Logic 82 (3):221-272.
    Using the theory of Borel equivalence relations we analyze the isomorphism relation on the countable models of a theory and develop a framework for measuring the complexity of possible complete invariants for isomorphism.
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  2.  98
    The Axiom of Determinancy Implies Dependent Choices in L(R).Alexander S. Kechris - 1984 - Journal of Symbolic Logic 49 (1):161 - 173.
    We prove the following Main Theorem: $ZF + AD + V = L(R) \Rightarrow DC$ . As a corollary we have that $\operatorname{Con}(ZF + AD) \Rightarrow \operatorname{Con}(ZF + AD + DC)$ . Combined with the result of Woodin that $\operatorname{Con}(ZF + AD) \Rightarrow \operatorname{Con}(ZF + AD + \neg AC^\omega)$ it follows that DC (as well as AC ω ) is independent relative to ZF + AD. It is finally shown (jointly with H. Woodin) that ZF + AD + ¬ DC (...)
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  3.  40
    New Directions in Descriptive Set Theory.Alexander S. Kechris - 1999 - Bulletin of Symbolic Logic 5 (2):161-174.
  4.  47
    Amenable Equivalence Relations and Turing Degrees.Alexander S. Kechris - 1991 - Journal of Symbolic Logic 56 (1):182-194.
  5.  8
    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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  6.  27
    Analytic Equivalence Relations and Ulm-Type Classifications.Greg Hjorth & Alexander S. Kechris - 1995 - Journal of Symbolic Logic 60 (4):1273-1300.
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  7.  21
    New Dichotomies for Borel Equivalence Relations.Greg Hjorth & Alexander S. Kechris - 1997 - Bulletin of Symbolic Logic 3 (3):329-346.
  8.  41
    The Prospects for Mathematical Logic in the Twenty-First Century.Samuel R. Buss, Alexander S. Kechris, Anand Pillay & Richard A. Shore - 2001 - Bulletin of Symbolic Logic 7 (2):169-196.
    The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.
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  9.  31
    Polish Metric Spaces: Their Classification and Isometry Groups.John D. Clemens, Su Gao & Alexander S. Kechris - 2001 - Bulletin of Symbolic Logic 7 (3):361-375.
  10. Π11 Borel Sets.Alexander S. Kechris, David Marker & Ramez L. Sami - 1989 - Journal of Symbolic Logic 54 (3):915 - 920.
  11.  24
    On Projective Ordinals.Alexander S. Kechris - 1974 - Journal of Symbolic Logic 39 (2):269-282.
  12.  5
    The Complexity of Antidifferentiation.Randall Dougherty, Alexander S. Kechris, Ferenc Beleznay & Matthew Foreman - 2001 - Bulletin of Symbolic Logic 7 (3):385-388.
  13.  42
    Amenable Versus Hyperfinite Borel Equivalence Relations.Alexander S. Kechris - 1993 - Journal of Symbolic Logic 58 (3):894-907.
    LetXbe a standard Borel space, and letEbe acountableBorel equivalence relation onX, i.e., a Borel equivalence relationEfor which every equivalence class [x]Eis countable. By a result of Feldman-Moore [FM],Eis induced by the orbits of a Borel action of a countable groupGonX.The structure of general countable Borel equivalence relations is very little understood. However, a lot is known for the particularly important subclass consisting of hyperfinite relations. A countable Borel equivalence relation is calledhyperfiniteif it is induced by a Borel ℤ-action, i.e., by (...)
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  14.  16
    Minimal Upper Bounds for Sequences of -Degrees.Alexander S. Kechris - 1978 - Journal of Symbolic Logic 43 (3):502-507.
  15.  14
    The Perfect Set Theorem and Definable Wellorderings of the Continuum.Alexander S. Kechris - 1978 - Journal of Symbolic Logic 43 (4):630-634.
    Let Γ be a collection of relations on the reals and let M be a set of reals. We call M a perfect set basis for Γ if every set in Γ with parameters from M which is not totally included in M contains a perfect subset with code in M. A simple elementary proof is given of the following result (assuming mild regularity conditions on Γ and M): If M is a perfect set basis for Γ, the field of (...)
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  16.  8
    Minimal Upper Bounds for Sequences of $Delta^1_{2n}$-Degrees.Alexander S. Kechris - 1978 - Journal of Symbolic Logic 43 (3):502-507.
  17.  7
    A Descriptive View of Ergodic Theory.Matthew Foreman, M. Foreman, A. S. Kechris, A. Louveau, B. Weiss & Alexander S. Kechris - 2001 - Bulletin of Symbolic Logic 7 (4):545-546.
  18.  8
    On Characterizing Spector Classes.Leo A. Harrington & Alexander S. Kechris - 1975 - Journal of Symbolic Logic 40 (1):19-24.
  19.  14
    We Announce Two New Dichotomy Theorems for Borel Equivalence Rela-Tions, and Present the Results in Context by Giving an Overview of Related Recent Developments. § 1. Introduction. For X a Polish (Ie, Separable, Completely Metrizable) Space and E a Borel Equivalence Relation on X, a (Complete) Classification. [REVIEW]Greg Hjorth & Alexander S. Kechris - 1997 - Bulletin of Symbolic Logic 3 (3).
  20.  51
    Annual Meeting of the Association for Symbolic Logic: Berkeley, 1990.Alexander S. Kechris - 1991 - Journal of Symbolic Logic 56 (1):361-371.
  21. Borel Hierarchy (Σ 0.Alexander S. Kechris - 1999 - Bulletin of Symbolic Logic 5 (2).
  22.  20
    Forcing with Δ Perfect Trees and Minimal Δ-Degrees.Alexander S. Kechris - 1981 - Journal of Symbolic Logic 46 (4):803 - 816.
  23.  20
    Forcing with \Triangle Perfect Trees and Minimal \Triangle-Degrees.Alexander S. Kechris - 1981 - Journal of Symbolic Logic 46 (4):803-816.
  24.  18
    In Memoriam: Gregory Hjorth 1963–2011.Alexander S. Kechris - 2011 - Bulletin of Symbolic Logic 17 (3):471-477.
  25.  10
    $Pi^1_1$ Borel Sets.Alexander S. Kechris, David Marker & Ramez L. Sami - 1989 - Journal of Symbolic Logic 54 (3):915-920.
  26.  10
    The Complexity of Topological Group Isomorphism.Alexander S. Kechris, André Nies & Katrin Tent - 2018 - Journal of Symbolic Logic 83 (3):1190-1203.
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  27.  7
    1996–1997 Winter Meeting of the Association for Symbolic Logic.Alexander S. Kechris - 1997 - Bulletin of Symbolic Logic 3 (3):367-377.
  28.  10
    The Largest Countable This, That, and the Other.Donald A. Martin, A. S. Kechris, D. A. Martin, Y. N. Moschovakis & Alexander S. Kechris - 1992 - Journal of Symbolic Logic 57 (1):262-264.
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  29.  10
    Ad and the Uniqueness of the Supercompact Measures on Pω 1.W. Hugh Woodin, A. S. Kechris, D. A. Martin, Y. N. Moschavokis & Alexander S. Kechris - 1992 - Journal of Symbolic Logic 57 (1):259-261.
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