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On recursion theory in IΣ1

Published online by Cambridge University Press:  12 March 2014

Petr Hájek  and
Antonín Kučera
Petr Hájek
Affiliation:
Mathematical Institute, Czechoslovak Academy of Sciences, 115 67 Prague, Czechoslovakia
Antonín Kučera
Affiliation:
Department of Cybernetics and Informatics, Charles University, 118 00 Prague 1, Czechoslovakia
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Abstract

It is shown that the low basis theorem is meaningful and provable in IΣ1 and that the priority-free solution to Post's problem formalizes in this theory.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 2 , June 1989 , pp. 576 - 589
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

Clotê, P. [1983], Partition relations in arithmetic, Methods in mathematical logic (proceedings of the sixth Latin American symposium, Caracas, 1983), Lecture Notes in Mathematics, vol. 1130, Springer-Verlag, Berlin, 1985, pp. 32–68.Google Scholar
Clote, P. [1985], Applications of the low-basis theorem in arithmetic, Recursion theory week (Oberwolfach, 1984), Lecture Notes in Mathematics, vol. 1141, Springer-Verlag, Berlin, 1985, pp. 65–88.CrossRefGoogle Scholar
Groszek, M. J. and Mytilinaios, M. E. [ta], Σ2-induction and the construction of a high degree (to appear).Google Scholar
Groszek, M.J. and Slaman, T. A. [ta-1], Foundations of the priority method. I: Finite and infinite injury (to appear).Google Scholar
Groszek, M.J. and Slaman, T. A., [ta-2], On Turing reducibility (to appear).Google Scholar
Jockusch, C. G. Jr., and Soare, R. I. [1972], classes and degrees of theories, Transactions of the American Mathematical Society, vol. 173, pp. 173–33.Google Scholar
Kučera, A. [1986], An alternative, priority-free, solution to Post's problem, Mathematical foundations of computer science 1986 (proceedings of the twelfth symposium, Bratislava), Lecture Notes in Computer Science, vol. 233, Springer-Verlag, Berlin, pp. 493–500.CrossRefGoogle Scholar
Mytilinaios, M. E. [1989], Finite injury and Σ 1-induction, this Journal, vol. 54, pp. 38–49.Google Scholar
Mytilinaios, M. E. and Slaman, T. A. [1988], Σ 2-collection and the infinite injury priority method, this Journal, vol. 53, pp. 212–221.Google Scholar
Paris, J. B. and Kirby, L. A. S. [1978], Σ n-collection schemas in arithmetic, Logic Colloquium '77, North-Holland, Amsterdam, 1978, pp. 199–209.CrossRefGoogle Scholar
Slaman, T. A. and Woodin, W. H. [ta], Σ1-collection and the finite injury priority method (to appear).Google Scholar