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Index sets for classes of high rank structures

  • W. Calvert (a1), E. Fokina (a2), S. S. Goncharov (a3), J. F. Knight (a4), O. Kudinov (a5), A. S. Morozov (a6) and V. Puzarenko (a7)...

This paper calculates, in a precise way. the complexity of the index sets for three classes of computable structures: the class of structures of Scott rank , the class , of structures of Scott rank , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete is m-complete relative to Kleene's and is m-complete relative to .

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[1] C. J. Ash and J. F. Knight , Pairs of recursive structures, Annals of Pure and Applied Logic, vol. 46 (1990), pp. 211234.

[3] J. Barwise , Admissible sets and structures: An approach to definability theory, Springer, 1975.

[6] W. Calvert , V. S. Harizanov , J. F. Knight , and S. Miller , Index sets for computable structures, Algebra and Logic, vol. 45 (2006), pp. 306325.

[10] J. Harrison , Recursive pseudo well-orderings, Transactions of the American Mathematical Society, vol. 131 (1968), pp. 526543.

[16] M. Nadel , Scott sentences and admissible sets, Annals of Mathematical Logic, vol. 7 (1974), pp. 267294.

[18] G. E. Sacks , Higher recursion theory, Springer-Verlag, 1990.

[21] W. White , On the complexity of categoricity in computable structures, Mathematical Logic Quarterly, vol. 49 (2003), pp. 603614.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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