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Isomorphism relations on computable structures

  • Ekaterina B. Fokina (a1), Sy-David Friedman (a1), Valentina Harizanov (a2), Julia F. Knight (a3), Charles Mccoy (a4) and Antonio Montalbán (a5)...

Abstract

We study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all equivalence relations on hyperarithmetical subsets of ω.

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[1] Ash, C. J. and Knight, J. F., Computable structures and the hyperarithmetical hierarchy, Elsevier, 2000.
[2] Calvert, W., Algebraic structure and computable structure, PhD Dissertation, University of Notre Dame, 2005.
[3] Calvert, W., Cenzer, D., Harizanov, V., and Morozov, A., Effective categoricity of equivalence structures, Annals of Pure and Applied Logic, vol. 141 (2006), pp. 6178.
[4] Calvert, W., Cummins, D., Knight, J. F., and Miller, S., Comparing classes of finite structures, Algebra and Logic, vol. 43 (2004), pp. 374392.
[5] Calvert, W., Knight, J., and Millar, J., Computable trees of Scott rank ωCK and computable approximations, this Journal, vol. 71 (2006), pp. 283298.
[6] Carson, J., Fokina, E., Harizanov, V. S., Knight, J. F., Quinn, S., Safranski, C., and Wallbaum, J., Computable embedding problem, submitted.
[7] Cenzer, D., Harizanov, V., and Remmel, J., and equivalence structures, Computability in Europe, 2009, Lecture Notes in Computer Science, vol. 5635, 2009, pp. 99108.
[8] Downey, R. and Montalban, A., The isomorphism problem for torsion-free Abelian groups is analytic complete, Journal of Algebra, vol. 320 (2008), pp. 22912300.
[9] Fokina, E. and Friedman, S., Equivalence relations on classes of computable structures, Computability in Europe, 2009, Lecture Notes in Computer Science, vol. 5635, 2009, pp. 198207.
[10] Fokina, E., equivalence relations on ω, submitted.
[11] Fokina, E., Friedman, S., and Törnquist, A., The effective theory of Borel equivalence relations, Annals of Pure and Applied Logic, vol. 161 (2010), pp. 837850.
[12] Fokina, E., Knight, J., Melnikov, A., Quinn, S., and Safranski, C., Ulm type, and coding rankhomogeneous trees in other structures, this Journal, vol. 76 (2011), pp. 846869.
[13] Friedman, H. and Stanley, L., A Borel reducibility theory for classes of countable structures, this Journal, vol. 54 (1989), pp. 894914.
[14] Friedman, S. D. and Ros, L. Motto, Analytic equivalence relations and bi-embeddability, this Journal, vol. 76 (2011), pp. 243266.
[15] Gao, S., Invariant descriptive set theory, Pure and Applied Mathematics, CRC Press/Chapman & Hall, 2009.
[16] Goncharov, S. S. and Knight, J. F., Computable structure and non-structure theorems, Algebra and Logic, vol. 41 (2002), pp. 351373, English translation.
[17] Harrison, J., Recursive pseudo well-orderings, Transactions of the American Mathematical Society, vol. 131 (1968), pp. 526543.
[18] Hjorth, G., The isomorphism relation on countable torsion-free Abelian groups, Fundamenta Mathematica, vol. 175 (2002), pp. 241257.
[19] Kanovei, V., Borel equivalence relations. Structure and classification, University Lecture Series 44, American Mathematical Society, 2008.
[20] Kaplansky, I., Infinite Abelian groups, University of Michigan Press, Ann Arbor, 1954.
[21] Kechris, A., New directions in descriptive set theory, The Bulletin of Symbolic Logic, vol. 5 (1999), no. 2, pp. 161174.
[22] Kechris, A. and Louveau, A., The classification of hypersmooth Borel equivalence relations, Journal of the American Mathematical Society, vol. 10 (1997), no. 1, pp. 215242.
[23] Khoussainov, B., Stephan, F., and Yang, Y., Computable categoricity and the Ershov hierarchy, Annals of Pure and Applied Logic, vol. 156 (2008), pp. 8695.
[24] Knight, J. F., Quinn, S. Miller, and Boom, M. Vanden, Turing computable embeddings, this Journal, vol. 73 (2007), pp. 901918.
[25] Louveau, A. and Rosendal, C., Complete analytic equivalence relations, Transactions of the American Mathematical Society, vol. 357 (2005), no. 12, pp. 48394866.
[26] Montalbán, A., On the equimorphism types of linear orderings, The Bulletin of Symbolic Logic, vol. 13 (2007), pp. 7199.
[27] Rogers, H., Theory of recursive functions and effective computability, McGraw-Hill, 1967.
[28] Rogers, L., Ulm's theorem for partially ordered structures related to simply presented Abelian p-groups, Transactions of the American Mathematical Society, vol. 227 (1977), pp. 333343.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
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