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Transactions of the American Mathematical Society

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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
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  • [1] A. Church, An unsolvable problem of elementary number theory, Amer. J. Math. vol. 58 (1936) pp. 345-363. MR 1507159
  • [2] K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik vol. 38 (1931) pp. 173-198. MR 1549910
  • [3] E. Hecke, Vorlesungen über die Theorie der algebraischen Zahlen, Leipzig, 1923.
  • [4] E. Landau, Über die Zerlegung total positiver Zahlen in Quadrate, Nach. Ges. Wiss. Göttingen, 1919, pp. 392-396.
  • [5] 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.
  • [6] 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.
  • [7] Julia Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic vol. 14 (1949) pp. 98-114. MR 0031446 (11:151f)
  • [8] B. Rosser, Extensions of some theorems of Gödel and Church, J. Symbolic Logic vol. 1 (1936) pp. 87-91.
  • [9] W. Szmielew, Decision problem in group theory, Proceedings of the Tenth International Congress of Philosophy, Amsterdam, 1948, pp. 763-766. MR 0028797 (10:500a)
  • [10] A. Tarski, A decision method for elementary algebra and geometry, Rand Corporation, Santa Monica, Calif., 1948. MR 0028796 (10:499f)
  • [11] -, On essential undecidability (abstract), J. Symbolic Logic vol. 14 (1949) pp. 75-76.
  • [12] -, Undecidability of group theory (abstract), J. Symbolic Logic vol. 14 (1949) pp. 76-77.

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DOI: https://doi.org/10.1090/S0002-9947-1951-0041081-0
Article copyright: © Copyright 1951 American Mathematical Society

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