Pacific Journal of Mathematics

Residue class domains of the ring of convergent sequences and of $C^\infty([0,1],{\bf R})$.

James J. Moloney

Article information

Source
Pacific J. Math., Volume 143, Number 1 (1990), 79-153.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102646204

Mathematical Reviews number (MathSciNet)
MR1047403

Zentralblatt MATH identifier
0731.54014

Subjects
Primary: 12J10: Valued fields
Secondary: 12L12: Model theory [See also 03C60] 54C30: Real-valued functions [See also 26-XX]

Citation

Moloney, James J. Residue class domains of the ring of convergent sequences and of $C^\infty([0,1],{\bf R})$. Pacific J. Math. 143 (1990), no. 1, 79--153. https://projecteuclid.org/euclid.pjm/1102646204


Export citation

References

  • [1] J. Ax and S. Kochen, Diophantine problems over localfields,II,Amer. J. Math., 87 (65), 631-648.
  • [2] D. Booth, Ph.D.Thesis, Univ. of Wisconsin, Madison, Wise. 1969.
  • [3] W. Baur, On the elementary theory of pairs of real closed fields, II, J. Symbolic Logic, 47 (1982), 669-679.
  • [4] C. C. Chang and H. J. Keisler, Model Theory, North Holland Publishing Co., Amsterdam, 1973.
  • [5] G. Cherlin, Rings of continuous functions: Decisionproblems, Model Theory of Algebra and Arithmetic 44-91, Lecture Notes in Math. 834, Springer, Berlin, 1980.
  • [6] G. Cherlin and M. Dickmann,Anneaux reel clos et anneaux des functions con- tinues, C. R. Acad. Sci. Paris Ser. A-B, 290 (1980), no. 1, A1-A4.
  • [7] G. Cherlin and M. Dickmann, Real Closed Rings II, Model Theory, Ann. Pure and Applied Logic, 25 (1983), 213-231.
  • [8] G. Cherlin and M. Dickmann, Real ClosedRings I, Residue rings of rings of continuous functions, Fund. Math., 126 (1986), 147-183.
  • [9] W. W. Comfort and S. Negrepontis, The Theory of Ultrafilters,Springer, New York, 1974.
  • [10] L. Gillman and M. Jerison, Rings of Continuous Functions, D. Van Nostrand Co., Princeton,N.J., 1960.
  • [11] M. Hendriksen and D. G. Johnson, On the structure of a class of Archimedean lattice-ordered algebras,Fund. Math., 50 (1961), 73-94.
  • [12] M. Henriksen, J. Isbell and D. G. Johnson,Residue classfields oflattice-ordered algebras,Fund. Math., 50 (1961), 107-117.
  • [13] N. Jacobson, Basic Algebra, II, W. H. Freeman and Co., San Francisco, 1980.
  • [14] S. Kochen, The Model Theory of Local Fields, Logic Conference Kiel 1974, 384-421, Lecture Notes in Math. 499, Springer, Berlin, 1975.
  • [15] C. W. Kohls, Ideals in rings of continuous functions, Fund. Math., 45 (1957), 28-50.
  • [16] C. W. Kohls, Prime ideals in rings of continuous functions, Illinois J. Math., 2 (1958), 505-536.
  • [17] C. W. Kohls, Prime ideals in rings of continuous functions II,Duke Math.J., 25 (1958), 447-458.
  • [18] C. W. Kohls, Prime z-filters on completely regular spaces, Trans. Amer. Math. Soc, 120(1965), 236-246.
  • [19] J. Moloney, First Order Theories of Residue Domains of Rings of Continuous Functions, Thesis, Rutgers University (1986).
  • [20] J. R. Munkres, Topology,a First Course,Prentice Hall, Inc. Englewood Cliffs, N.J., 1975.
  • [21] W. Rudin, Homogeneity problems in the theory ofCech compactifications,Duke Math. J., 23(1956), 409-416.
  • [22] A. Tarski, A Decision Model for Elementary Algebra and Geometry, University of California Press, Berkeley, 1951.
  • [23] J. Van Mill, An Introduction to , Handbook of Set Theoretic Topology, 503-567, North-Holland,Amsterdam, 1984.
  • [24] E. Wimmers, The Shelah P-point Independence Theorem, Israel J. Math., 43 (1982), 28-48.