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Transactions of the American Mathematical Society

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Rings of continuous integer-valued functions and nonstandard arithmetic


Author: Norman L. Alling
Journal: Trans. Amer. Math. Soc. 118 (1965), 498-525
MSC: Primary 13.20; Secondary 02.00
DOI: https://doi.org/10.1090/S0002-9947-1965-0184960-6
MathSciNet review: 0184960
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  • [A$ _{1}$] N. L. Alling, A characterization of Abelian $ {\eta _\alpha }$-groups in terms of their natural valuation, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 711-713. MR 0175983 (31:259)
  • [A$ _{2}$] -, On the existence of real-closed fields that are $ {\eta _\alpha }$-sets of power $ {\aleph _\alpha }$, Trans. Amer. Math. Soc. 103 (1962), 341-352. MR 0146089 (26:3615)
  • [A$ _{3}$] -, An application of valuation theory to rings of continuous real and complex-valued functions, Trans. Amer. Math. Soc. 109 (1963), 492-508. MR 0154886 (27:4830)
  • [A$ _{4}$] -, The valuation theory of meromorphic function fields over open Riemann surfaces, Acta Math. 110 (1963), 79-96. MR 0160781 (28:3992)
  • [B] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ. Vol. 25, Amer. Math. Soc., Providence, R. I., 1960.
  • [ES] S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton Univ. Press, Princeton, N. J., 1952. MR 0050886 (14:398b)
  • [GJ] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
  • [H$ _{1}$] F. Hausdorff, Grundzüge der Mengenlehre (Leipzig, 1914), Chelsea, New York, 1949.
  • [H$ _{2}$] L. Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64, (1948), 45-99. MR 0026239 (10:126e)
  • [K] S. Kochen, Ultraproducts in the theory of models, Ann. of Math. (2) 74 (1961), 221-261. MR 0138548 (25:1992)
  • [P] R. S. Pierce, Rings of integer-valued continuous functions, Trans. Amer. Math. Soc. 100 (1961), 371-394. MR 0131438 (24:A1289)
  • [R] A. Robinson, Introduction to model theory and the metamathematics of algebra, North-Holland, Amsterdam, 1963. MR 0153570 (27:3533)
  • [S] D. Scott, On constructing models for arithmetic, Infinistic methods, Internat. Math. Union, Warsaw, 1961. MR 0152445 (27:2423)
  • [ZS$ _{1}$] R. Zariski and P. Samuel, Commutative algebra. I, Van Nostrand, Princeton, N. J. 1958.
  • [ZS$ _{2}$] -, Commutative algebra. II, Van Nostrand, Princeton, N.J., 1960.

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DOI: https://doi.org/10.1090/S0002-9947-1965-0184960-6
Article copyright: © Copyright 1965 American Mathematical Society

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