Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Some properties of pseudo-complements of recursively enumerable sets


Author: Robert A. Di Paola
Journal: Trans. Amer. Math. Soc. 121 (1966), 296-308
MSC: Primary 02.70
DOI: https://doi.org/10.1090/S0002-9947-1966-0195722-9
MathSciNet review: 0195722
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] M. Davis, Computability and unsolvability, McGraw-Hill, New York, 1958. MR 0124208 (23:A1525)
  • [2] -, On the theory of recursive unsolvability, Doctoral dissertation, Princeton University, Princeton, N. J., 1950.
  • [3] -, Pseudo-complements of recursively enumerable sets, Abstract 299, Bull. Amer. Math. Soc. 60 (1954), 169-170.
  • [4] -, Arithmetical problems and recursively enumerable predicates, J. Symbolic Logic 18 (1953), 33-41. MR 0055281 (14:1052c)
  • [5] R. A. Di Paola, On pseudo-complements of recursively enumerable sets, Doctoral dissertation, Belfer Graduate School of Science, Yeshiva University, New York, 1964.
  • [6] A. Ehrenfeucht and S. Feferman, Representability of recursively enumerable sets in formal theories, Arch. Math. Logik Grundlagenforsch. 5 (1960), 37-41. MR 0125791 (23:A3088)
  • [7] S. Feferman, Arithmetization of metamathematics in a general setting, Fund. Math. 49 (1960/1961), 35-92. MR 0147397 (26:4913)
  • [8] -, Transfinite recursive progressions of axiomatic theories, J. Symbolic Logic 27 (1962), 259-316. MR 0172792 (30:3011)
  • [9] -, Degrees of unsolvability associated with classes of formalized theories, J. Symbolic Logic 22 (1957), 161-175. MR 0098675 (20:5130)
  • [10] S. C. Kleene, Introduction to metamathematics, Van Nostrand, Princeton, N. J., 1952. MR 0051790 (14:525m)
  • [11] -, On the forms of the predicates in the theory of constructive ordinals, Amer. J. Math. 77 (1955), 405-428. MR 0070595 (17:5a)
  • [12] J. Myhill, Creative sets, Z. Math. Logik Grundlagen Math. 1 (1955), 97-108. MR 0071379 (17:118g)
  • [13] H. Putnam and R. Smullyan, Exact separation of recursively enumerable sets within theories, Proc. Amer. Math. Soc. 11 (1960), 574-577. MR 0120150 (22:10907)
  • [14] H. Rogers, Computing degrees of unsolvability, Math. Ann. 138 (1959), 125-140. MR 0114752 (22:5571)
  • [15] J. B. Rosser, Extensions of some theorems of Gödel and Church, J. Symbolic Logic 1 (1936), 87-91.
  • [16] R. Smullyan, Theory of formal systems, Annals of Mathematics Studies No. 47, Princeton Univ. Press, Princeton, N. J., 1961. MR 0121300 (22:12042)
  • [17] A. Tarski, A. Mostowski and R. Robinson, Undecidable theories studies in logic and the foundations of mathematics, North-Holland, Amsterdam, 1953. MR 0058532 (15:384h)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 02.70

Retrieve articles in all journals with MSC: 02.70


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1966-0195722-9
Article copyright: © Copyright 1966 American Mathematical Society

American Mathematical Society