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)

 
 

 

Undecidable rings


Author: Raphael M. Robinson
Journal: Trans. Amer. Math. Soc. 70 (1951), 137-159
MSC: Primary 02.0X
DOI: https://doi.org/10.1090/S0002-9947-1951-0041081-0
MathSciNet review: 0041081
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • Alonzo Church, An Unsolvable Problem of Elementary Number Theory, Amer. J. Math. 58 (1936), no. 2, 345–363. MR 1507159, DOI https://doi.org/10.2307/2371045
  • Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, DOI https://doi.org/10.1007/BF01700692
  • E. Hecke, Vorlesungen über die Theorie der algebraischen Zahlen, Leipzig, 1923. E. Landau, Über die Zerlegung total positiver Zahlen in Quadrate, Nach. Ges. Wiss. Göttingen, 1919, pp. 392-396. A. Mostowski and A. Tarski, Undecidability in the arithmetic of integers and in the theory of rings (abstract), J. Symbolic Logic vol. 14 (1949) p. 76. M. Presburger, Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt, Comptes-rendus du I Congrès des Mathématiciens des Pays Slaves, Warsaw, 1929, pp. 92-101, 395.
  • Julia Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic 14 (1949), 98–114. MR 31446, DOI https://doi.org/10.2307/2266510
  • B. Rosser, Extensions of some theorems of Gödel and Church, J. Symbolic Logic vol. 1 (1936) pp. 87-91.
  • W. Szmielew, Decision problem in group theory, Library of the Tenth International Congress of Philosophy, Amsterdam, August 11–18, 1948, Vol.1, Proceedings of the Congress, publisher unknown, 1949, pp. 763–766. MR 0028797
  • Alfred Tarski, A Decision Method for Elementary Algebra and Geometry, RAND Corporation, Santa Monica, Calif., 1948. MR 0028796
  • ---, On essential undecidability (abstract), J. Symbolic Logic vol. 14 (1949) pp. 75-76. ---, Undecidability of group theory (abstract), J. Symbolic Logic vol. 14 (1949) pp. 76-77.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 02.0X

Retrieve articles in all journals with MSC: 02.0X


Additional Information

Article copyright: © Copyright 1951 American Mathematical Society