## Rings of continuous integer-valued functions and nonstandard arithmetic

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- by Norman L. Alling
- Trans. Amer. Math. Soc.
**118**(1965), 498-525 - DOI: https://doi.org/10.1090/S0002-9947-1965-0184960-6
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## References

- Norman 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**175983**, DOI 10.1073/pnas.47.5.711 - Norman L. Alling,
*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**146089**, DOI 10.1090/S0002-9947-1962-0146089-X - Norman L. Alling,
*An application of valuation theory to rings of continuous real and complex-valued functions*, Trans. Amer. Math. Soc.**109**(1963), 492–508. MR**154886**, DOI 10.1090/S0002-9947-1963-0154886-0 - Norman L. Alling,
*The valuation theory of meromorphic function fields over open Riemann surfaces*, Acta Math.**110**(1963), 79–96. MR**160781**, DOI 10.1007/BF02391855
G. Birkhoff, - Samuel Eilenberg and Norman Steenrod,
*Foundations of algebraic topology*, Princeton University Press, Princeton, N.J., 1952. MR**0050886** - Leonard Gillman and Meyer Jerison,
*Rings of continuous functions*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0116199**
F. Hausdorff, - Edwin Hewitt,
*Rings of real-valued continuous functions. I*, Trans. Amer. Math. Soc.**64**(1948), 45–99. MR**26239**, DOI 10.1090/S0002-9947-1948-0026239-9 - Simon Kochen,
*Ultraproducts in the theory of models*, Ann. of Math. (2)**74**(1961), 221–261. MR**138548**, DOI 10.2307/1970235 - R. S. Pierce,
*Rings of integer-valued continuous functions*, Trans. Amer. Math. Soc.**100**(1961), 371–394. MR**131438**, DOI 10.1090/S0002-9947-1961-0131438-8 - Abraham Robinson,
*Introduction to model theory and to the metamathematics of algebra*, North-Holland Publishing Co., Amsterdam, 1963. MR**0153570** - Dana Scott,
*On constructing models for arithmetic*, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Pergamon, Oxford; Państwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 235–255. MR**0152445**
R. Zariski and P. Samuel,

*Lattice theory*, Amer. Math. Soc. Colloq. Publ. Vol. 25, Amer. Math. Soc., Providence, R. I., 1960.

*Grundzüge der Mengenlehre*(Leipzig, 1914), Chelsea, New York, 1949.

*Commutative algebra*. I, Van Nostrand, Princeton, N. J. 1958. —,

*Commutative algebra*. II, Van Nostrand, Princeton, N.J., 1960.

## Bibliographic Information

- © Copyright 1965 American Mathematical Society
- 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