Journal of Symbolic Logic

Π11 relations and paths through 𝒪

Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight, and Richard A. Shore

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

J. Symbolic Logic Volume 69, Issue 2 (2004), 585-611.

First available in Project Euclid: 19 April 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Goncharov, Sergey S.; Harizanov, Valentina S.; Knight, Julia F.; Shore, Richard A. Π 1 1 relations and paths through 𝒪. J. Symbolic Logic 69 (2004), no. 2, 585--611. doi:10.2178/jsl/1082418544.

Export citation


  • C. J. Ash and J. F. Knight Possible degrees in recursive copies, Annals of Pure and Applied Logic, vol. 75 (1995), pp. 215--221.
  • C. J. Ash, J. F. Knight, M. Manasse, and T. Slaman Generic copies of countable structures, Annals of Pure and Applied Logic, vol. 42 (1989), pp. 195--205.
  • C. J. Ash and A. Nerode Intrinsically recursive relations, Aspects of effective algebra (J. N. Crossley, editor), Steel's Creek, Australia, Upside Down A Book Co.,1981, pp. 26--41.
  • E. Barker Intrinsically $\Sigma_\alpha ^0$ relations, Annals of Pure and Applied Logic, vol. 39 (1988), pp. 105--130.
  • J. Barwise Infinitary logic and admissible sets, Journal of Symbolic Logic, vol. 34 (1969), pp. 226--252.
  • J. Chisholm Effective model theory vs. recursive model theory, Journal of Symbolic Logic, vol. 55 (1990), pp. 1168--1191.
  • R. Downey, C. G. Jockusch, Jr., and M. Stob Array nonrecursive degrees and genericity, Computability, enumerability, unsolvability, London Mathematical Society Lecture Notes Series, vol. 224, Cambridge University Press,1996, pp. 93--104.
  • H. Friedman One hundred and two problems in mathematical logic, Journal of Symbolic Logic, vol. 40 (1975), pp. 113--129.
  • S. S. Goncharov The quantity of nonautoequivalent constructivizations, Algebra and Logic, vol. 16 (1977), pp. 169--185, English translation.
  • S. S. Goncharov, V. S. Harizanov, J. F. Knight, C. McCoy, R. G. Miller, and R. Solomon Enumerations in computable structure theory, submited.
  • S. S. Goncharov and J. F. Knight Computable structure and non-structure theorems, Algebra and Logic, vol. 41 (2002), pp. 351--373, English translation.
  • V. S. Harizanov Some effects of Ash-Nerode and other decidability conditions on degree spectra, Annals of Pure and Applied Logic, vol. 55 (1991), pp. 51--65.
  • L. Harrington McLaughlin's conjecture, handwritten notes,1976.
  • J. Harrison Recursive pseudo-well-orderings, Transactions of the American Mathematical Society, vol. 131 (1968), pp. 526--543.
  • D. R. Hirschfeldt, B. Khoussainov, R. A. Shore, and A. M. Slinko Degree spectra and computable dimensions in algebraic structures, Annals of Pure and Applied Logic, vol. 115 (2002), pp. 71--113.
  • C. G. Jockusch, Jr. Recursiveness of initial segments of Kleene's $\mathcalO$, Fundamenta Mathematicae, vol. 87 (1975), pp. 161--167.
  • C. G. Jockusch, Jr. and T. G. McLaughlin Countable retracing functions and $\Pi _2^0$ predicates, Pacific Journal of Mathematics, vol. 30 (1969), pp. 67--93.
  • I. Kaplansky Infinite abelian groups, University of Michigan Press,1954.
  • B. Khousainov and R. A. Shore Computable isomorphisms, degree spectra of relations and Scott families, Annals of Pure and Applied Logic, vol. 93 (1998), pp. 153--193.
  • G. Kreisel Set theoretic problems suggested by the notion of potential totality, Infinitistic methods, Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 1959, Pergamon,1961, pp. 103--140.
  • A. H. Lachlan Solution to a problem of Spector, Canadian Journal of Mathematics, vol. 23 (1971), pp. 247--256.
  • M. Lerman Degrees of unsolvability, Springer-Verlag, Berlin,1983.
  • M. S. Manasse Techniques and counterexamples in almost categorical recursive model theory, Ph.D. thesis, University of Wisconsin-Madison,1982.
  • R. Parikh A note on paths through $\mathcalO $, Proceedings of the American Mathematical Society, vol. 39 (1973), pp. 178--180.
  • J. P. Ressayre Models with compactness properties relative to an admissible language, Annals of Mathematical Logic, vol. 11 (1977), pp. 31--55.
  • H. Rogers, Jr. Theory of recursive functions and effective computability, McGraw-Hill, New York,1967.
  • G. E. Sacks On the number of countable models, Southeast Asian Conference on Logic (Singapore, 1981) (C. T. Chong and M. J. Wicks, editors), North-Holland,1983, pp. 185--195.
  • D. Scott Logic with denumerably long formulas and finite strings of quantifiers, The theory of models (J. W. Addison, L. Henkin, and A. Tarski, editors), Proc. 1963 Internat. Sympos. Berkeley, North-Holland,1965, pp. 329--341.
  • I. N. Soskov Intrinsically hyperarithmetical sets, Mathematical Logic Quarterly, vol. 42 (1996), pp. 469--480.
  • C. Spector Recursive well-orderings, Journal of Symbolic Logic, vol. 20 (1955), pp. 151--163.
  • J. R. Steel Forcing with tagged trees, Annals of Mathematical Logic, vol. 15 (1978), pp. 55--74.