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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Undecidable rings
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by Raphael M. Robinson PDF
Trans. Amer. Math. Soc. 70 (1951), 137-159 Request permission
References
  • Alonzo Church, An Unsolvable Problem of Elementary Number Theory, Amer. J. Math. 58 (1936), no. 2, 345–363. MR 1507159, DOI 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 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 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. I, Proceedings of the Congress, publisher unknown, 1949, pp. 763–766. MR 0028797
  • Alfred Tarski, A Decision Method for Elementary Algebra and Geometry, The 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.
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Additional Information
  • © Copyright 1951 American Mathematical Society
  • 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