Skip to main content

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 .

Hide All
[1]Ash, C. J. and Knight, J. F., Pairs of recursive structures, Annals of Pure and Applied Logic, vol. 46 (1990), pp. 211234.
[2]Ash, C. J. and Knight, J. F., Computable structures and the hyperarithmetical hierarchy, Elsevier, 2000.
[3]Barwise, J., Admissible sets and structures: An approach to definability theory, Springer, 1975.
[4]Calvert, W., Goncharov, S. S., and Knight, J. F., Boolean algebras of Scott rank , preprint.
[5]Calvert, W., Goncharov, S. S., and Knight, J. F., Computable structures of Scott rank in familiar classes, Proceedings of the North Texas Logic Conference, October, 2004, Contemporary Mathematics, American Mathematical Society, to appear in Advances in Logic.
[6]Calvert, W., Harizanov, V. S., Knight, J. F., and Miller, S., Index sets for computable structures, Algebra and Logic, vol. 45 (2006), pp. 306325.
[7]Calvert, W., Knight, J. F., and Millar, J., Trees of Scott rank and computable approximability, this Journal, vol. 71 (2006), pp. 283298.
[8]Goncharov, S. S., Harizanov, V. S., Knight, J. F., and Shore, R., relations and paths through , this Journal, vol. 69 (2004), pp. 585611.
[9]Goncharov, S. S. and Knight, J. F., Computable structure and non-structure theorems, Algebra and Logic, vol. 41 (2002), pp. 351373.
[10]Harrison, J., Recursive pseudo well-orderings, Transactions of the American Mathematical Society, vol. 131 (1968), pp. 526543.
[11]Keisler, H. J., Model theory for infinitary logic, North-Holland, 1971.
[12]Knight, J. F., A computable structure of Scott rank whose computable infinitary theory is not ℵ0 categorical, in preparation.
[13]Knight, J. F. and Millar, J., Computable structures of rank , Journal of Mathematical Logic, submitted.
[14]Makkai, M., An example concerning Scott heights, this Journal, vol. 46 (1981), pp. 301318.
[15]Millar, J. and Sacks, G., Atomic models higher up, preprint.
[16]Nadel, M., Scott sentences and admissible sets, Annals of Mathematical Logic, vol. 7 (1974), pp. 267294.
[17]Rogers, H. Jr., Theory of recursive functions and effective comput ability, McGraw-Hill, 1967.
[18]Sacks, G. E., Higher recursion theory, Springer-Verlag, 1990.
[19]Scott, D., Logic with denumerably long formulas and finite strings of quantifiers, The theory of models (Addison, J., Henkin, L., and Tarski, A., editors), North-Holland, 1965, pp. 329341.
[20]White, W., Characterizations for computable structures, PhD dissertation, Cornell University, 2000.
[21]White, W., On the complexity of categoricity in computable structures, Mathematical Logic Quarterly, vol. 49 (2003), pp. 603614.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *