Index sets for Π01 classes

Annals of Pure and Applied Logic

Volumn 93, Issue 1-3, 1998, Pages 3-61

  Cenzer, Douglas ^a   Remmel, Jeffrey ^b  

^a UNIVERSITY OF FLORIDA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Index sets; 01 classes

Indexed keywords

EID: 0032574620     PISSN: 01680072     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-0072(97)00052-3     Document Type: Article

References (36)

1. [1] D. Bean, Effective coloration, J. Symbolic Logic 41 (1976) 469-480.
2. [2] R. Beigel, W. Gasarch, On the complexity of finding the chromatic number of a recursive graph I, Ann. Pure Appl. Logic 45 (1989) 1-38.
3. [3] R. Beigel, W. Gasarch, On the complexity of finding the chromatic number of a recursive graph II, Ann. Pure Appl. Logic 45 (1989) 227-247.
4. 1 classes, Ann. Pure Appl. Logic 31 (1986) 145-163.
5. 1 classes, Ann. Pure Appl. Logic 59 (1993) 79-139.
6. [6] D. Cenzer, R. Mauldin, On the Borel class of the derived set operator, Bull. Soc. Math. France 110 (1982) 357-380, II, 111 (1983) 367-372.
7. [6] D. Cenzer, R. Mauldin, On the Borel class of the derived set operator, Bull. Soc. Math. France 110 (1982) 357-380, II, 111 (1983) 367-372.
8. 1 classes in mathematics, in: Y. Ershov, S. Goncharov, A. Nerode, J. Remmel (Eds.), Handbook of Recursive Mathematics, to appear.
9. [8] A. Ehrenfeucht, Separable theories, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961) 17-19.
10. [9] L. Feiner, Hierarchies of Boolean algebras, J. Symbolic Logic 35 (1970) 365-374.
11. [10] W. Gasarch, A survey of recursive combinatorics, in: Y. Ershov, S. Goncharov, A. Nerode, J. Remmel (Eds.), Handbook of Recursive Mathematics, to appear.
12. [11] W. Gasarch, G. Martin, Index sets in recursive combinatorics, in: J. Crossley, J. Remmel, R. Shore, M. Sweedler (Eds.), Logical Methods (in honor of A. Nerode), Progress in Comp. Sci and Appl. Logic, vol. 12, Birkhauser, Basal, 1993, pp. 352-385.
13. [12] L. Hay, Index sets of finite classes of recursively enumerable sets, J. Symbolic Logic 34 (1969) 39-44.
14. [13] L. Hay, D. Miller, A topological analog to the Rice-Shapiro index theorem, J. Symbolic Logic 47 (1982) 824-832.
15. 1 X}, J. Symbolic Logic 51 (1986) 110-116.
16. [15] P.G. Hinman, Recursion-Theoretic Hierarchies, Springer, Berlin, 1978.
17. 1 classes and Rado's selection principle, J. Symbolic Logic 56 (1991) 684-693.
18. 1 classes and degrees of theories, Trans. Amer. Math. Soc. 173 (1972) 33-56.
19. 1 classes, Pacific J. Math. 40 (1972) 605-616.
20. [19] S. Kleene, Hierarchies of number-theoretic predicates, Bull Amer. Math. Soc. 61 (1955) 193-213.
21. [20] G. Kreisel, Analysis of the Cantor-Bendixson theorem by means of the analytic hierarchy, Bull. Acad. Polon. Sciences, Ser. Math. Astronom. Phys. 7 (1959) 621-626.
22. X, Lecture Notes in Math., vol. 171, Springer, Berlin, 1970, pp. 45-48.
23. [22] S. Lempp, Hyperarithmetical index sets in recursion theory, Trans. Amer. Math. Soc. 303 (1987) 559-583.
24. [23] A. Manaster, J. Rosenstein, Effective matching, Proc. London Math. Soc. 25 (1972) 615-654.
25. [24] D. Martin, M. Pour-El, Axiomatizable theories with few axiomatizable extensions, J. Symbolic Logic 35 (1970) 205-209.
26. [25] P. Odifreddi, Classical Recursion Theory, North-Holland, Amsterdam, 1989.
27. [26] J. Remmel, On the effectiveness of the Schroder-Bernstein theorem, Proc. Amer. Math. Soc. 83 (1981) 379-386.
28. 1 classes, Ann. Pure Appl. Logic 32 (1986) 185-194.
29. [28] B.J. Rosser, Extensions of some theorems of Gödel and Church, J. Symbolic Logic 1 (1936) 87-91.
30. [29] S. Schwarz, Index sets of recursively enumerable sets, quotient lattices and recursive linear orderings, Ph.D. Dissertation, University of Chicago, 1982.
31. [30] V. Selivanov, Index sets in the hyperarithmetical hierarchy, Sib. Math. J. 25 (1984) 474-488.
32. [31] V. Selivanov, Index sets of classes of hyperhypersimple sets, Algebra Logic 29 (1990) 155-168.
33. [32] V. Selivanov, Fine hierarchies and definable index sets, Algebra Logic 30 (1991) 463-475.
34. [33] J.R. Shoenfield, Degrees of formal systems, J. Symbolic Logic 23 (1958) 389-392.
35. [34] R. Soare, Recursively Enumerable Sets and Degrees, Springer, Berlin, 1987.
36. [35] J. Thurber, Recursive and r.e. quotient Boolean algebras, Arch. Math. Logic 33 (2) (1994) 121-129.