32 found
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  1. Alexander S. Kechris, David Marker & Ramez L. Sami (1989). Π11 Borel Sets. Journal of Symbolic Logic 54 (3):915 - 920.
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  2.  18
    Alexander S. Kechris (1999). New Directions in Descriptive Set Theory. Bulletin of Symbolic Logic 5 (2):161-174.
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  3.  13
    Greg Hjorth & Alexander S. Kechris (1997). New Dichotomies for Borel Equivalence Relations. Bulletin of Symbolic Logic 3 (3):329-346.
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  4. Greg Hjorth & Alexander S. Kechris (1996). Borel Equivalence Relations and Classifications of Countable Models. 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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  5.  6
    Alexander S. Kechris (1973). Measure and Category in Effective Descriptive Set Theory. Annals of Mathematical Logic 5 (4):337-384.
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  6.  69
    Alexander S. Kechris (1984). The Axiom of Determinancy Implies Dependent Choices in L(R). 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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  7.  14
    Alexander S. Kechris (1991). Amenable Equivalence Relations and Turing Degrees. Journal of Symbolic Logic 56 (1):182-194.
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  8.  17
    John D. Clemens, Su Gao & Alexander S. Kechris (2001). Polish Metric Spaces: Their Classification and Isometry Groups. Bulletin of Symbolic Logic 7 (3):361-375.
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  9.  4
    Greg Hjorth, Alexander S. Kechris & Alain Louveau (1998). Borel Equivalence Relations Induced by Actions of the Symmetric Group. 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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  10.  19
    Greg Hjorth & Alexander S. Kechris (1995). Analytic Equivalence Relations and Ulm-Type Classifications. Journal of Symbolic Logic 60 (4):1273-1300.
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  11. Leo A. Harrington & Alexander S. Kechris (1981). On the Determinacy of Games on Ordinals. Annals of Mathematical Logic 20 (2):109-154.
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  12.  19
    Samuel R. Buss, Alexander S. Kechris, Anand Pillay & Richard A. Shore (2001). The Prospects for Mathematical Logic in the Twenty-First Century. 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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  13.  7
    Alexander S. Kechris (1993). Amenable Versus Hyperfinite Borel Equivalence Relations. Journal of Symbolic Logic 58 (3):894-907.
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  14.  7
    Alexander S. Kechris (1981). Forcing with ▵ Perfect Trees and Minimal ▵-Degrees. Journal of Symbolic Logic 46 (4):803 - 816.
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  15.  7
    Greg Hjorth & Alexander S. Kechris (1997). 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] Bulletin of Symbolic Logic 3 (3).
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  16.  2
    Alexander S. Kechris (1978). Countable Ordinals and the Analytical Hierarchy, II. Annals of Mathematical Logic 15 (3):193-223.
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  17.  4
    Alexander S. Kechris (1978). Minimal Upper Bounds for Sequences of Δ12n-Degrees. Journal of Symbolic Logic 43 (3):502 - 507.
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  18.  5
    Alexander S. Kechris (2011). In Memoriam: Gregory Hjorth 1963—2011. Bulletin of Symbolic Logic 17 (3):471-477.
  19.  9
    Alexander S. Kechris (1974). On Projective Ordinals. Journal of Symbolic Logic 39 (2):269-282.
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  20.  20
    Alexander S. Kechris (1991). Annual Meeting of the Association for Symbolic Logic: Berkeley, 1990. Journal of Symbolic Logic 56 (1):361-371.
  21.  3
    Alexander S. Kechris (1981). Forcing with \Triangle Perfect Trees and Minimal \Triangle-Degrees. Journal of Symbolic Logic 46 (4):803-816.
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  22.  5
    Alexander S. Kechris (1978). The Perfect Set Theorem and Definable Wellorderings of the Continuum. 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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  23.  3
    Leo A. Harrington & Alexander S. Kechris (1975). On Characterizing Spector Classes. Journal of Symbolic Logic 40 (1):19-24.
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  24.  1
    Alexander S. Kechris (1978). Minimal Upper Bounds for Sequences of $Delta^1_{2n}$-Degrees. Journal of Symbolic Logic 43 (3):502-507.
  25. Howard S. Becker, R. Dougherty, A. S. Kechris, Alexander S. Kechris, Alain Louveau & A. Louveau (2002). Hausdorff Measures and Sets of Uniqueness for Trigonometric SeriesCovering Theorems for Uniqueness and Extended Uniqueness SetsHereditary Properties of the Class of Closed Sets of Uniqueness for Trigonometric SeriesDescriptive Set Theory and Harmonic Analysis. Bulletin of Symbolic Logic 8 (1):94.
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  26. Randall Dougherty, Alexander S. Kechris, Ferenc Beleznay & Matthew Foreman (2001). The Complexity of Antidifferentiation. Bulletin of Symbolic Logic 7 (3):385-388.
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  27. Matthew Foreman, M. Foreman, A. S. Kechris, A. Louveau, B. Weiss & Alexander S. Kechris (2001). A Descriptive View of Ergodic Theory. Bulletin of Symbolic Logic 7 (4):545-546.
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  28. Alexander S. Kechris (1999). Borel Hierarchy (Σ 0. Bulletin of Symbolic Logic 5 (2).
     
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  29. Alexander S. Kechris, Yiannis N. Moschovakis, A. S. Kechris & Y. N. Moschovakis (1985). Cobol Seminar. Journal of Symbolic Logic 50 (3):849-851.
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  30. Alexander S. Kechris (1978). Minimal Upper Bounds for Sequences of -Degrees. Journal of Symbolic Logic 43 (3):502-507.
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  31. Alexander S. Kechris, David Marker & Ramez L. Sami (1989). $Pi^1_1$ Borel Sets. Journal of Symbolic Logic 54 (3):915-920.
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  32. Alexander S. Kechris (1997). 1996-1997 Winter Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 3 (3):367-377.
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