References
Kleene, S.: Recursive predicates and quantifiers. Trans. Amer. math. Soc.53, 41–73 (1943).
Mostowski, A.: On definable sets of positive integers. Fund. math.34, 81–112 (1947).
Post, E.: Recursively enumerable sets of positive integers and their decision problems. Bull. Amer. Math. Soc.50, 284–316 (1944).
Kleene, S., andE. Post: The upper semi-lattice of degrees of recursive unsolvability. Ann. of Math. ser. 2,59, 379–407 (1954).
Turing, A.: On computable numbers with an application to the Entscheidungsproblem. Proc. London math. Soc., ser. 2,42, 230–265 (1936/37).
Friedberg, R.: Two recursively enumerable sets of incomparable degrees of unsolvability. Proc. Nat. Acad. Sci. (Wash.)43, 236–238 (1957).
Mostowski, A.: Examples of sets definable by means of two and three quantifiers. Fund. math.42, 259 bis 270 (1955).
Robinson, R.: Arithmetical representation of recursively enumerable sets. J. Symb. Log.21, 162–186 (1956).
Davis, M.: Computability and Unsolvability. New York: McGraw-Hill 1958.
Rogers, H.: Gödel numberings of partial recursive functions. J. Symb. Log.23, 331–341 (1958).
Friedberg, R., andH. Rogers: Reducibility and completeness for sets of integers. Z. math. Log.5, H. 2 (1959).
Myhill, J.: Creative sets. Z. math. Log.1, 97–108 (1955).
Spector, C.: On degrees of resursive unsolvability. Ann. of Math., ser. 2,64, 581–592 (1956).
Shapiro, N.: Degrees of computability. Trans. Amer. math. Soc.82, 281–299 (1956).
Tarski, A.: Sur les ensembles définissables de nombres réels I. Fund. math.17, 210–239 (1931).
Dekker, J.: A theorem on hypersimple sets. Proc. Amer. math. Soc.5, 791–796 (1954).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rogers, H. Computing degrees of unsolvability. Math. Ann. 138, 125–140 (1959). https://doi.org/10.1007/BF01342939
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01342939