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First-order topological axioms

Published online by Cambridge University Press:  12 March 2014

R. D. Kopperman
R. D. Kopperman*
Affiliation:
City University of New York, New York, New York 10031
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Abstract

We exhibit a finite list of first-order axioms which may be used to define topological spaces. For most separation axioms we discover a first-order equivalent statement.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 3 , September 1981 , pp. 475 - 489
Copyright
Copyright © Association for Symbolic Logic 1981

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References

REFERENCES

[1]Ax, J. and Kochen, S., Diophantine problems over local fields. I, American Journal of Mathematics, vol. 87 (1965), pp. 605–630.CrossRefGoogle Scholar
[2]Ax, J. and Kochen, S., Diophantine problems over local fields. II, American Journal of Mathematics, vol. 87 (1965), pp. 631–648.CrossRefGoogle Scholar
[3]Ax, J. and Kochen, S., Diophantine problems over local fields. III, American Journal of Mathematics, vol. 82 (1966), pp. 432–456.Google Scholar
[4]Chang, C. C. and Morel, A., On closure under direct product, this Journal, vol. 23 (1958), pp. 149–154.Google Scholar
[5]Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955.Google Scholar
[6]Kopperman, R., Model theory and its applications, Allyn & Bacon, Boston, 1972.Google Scholar
[7]Kopperman, R., On the axiomatizability of uniform spaces, this Journal, vol. 32 (1967), pp. 289–294.Google Scholar
[8]Kopperman, R., Applications of infinitary languages to analysis, Applications of model theory to algebra, analysis, and probability (Luxemburg, W.A.J., Editor), Holt, Reinhart and Winston, New York, 1969.Google Scholar
[9]Kopperman, R., Continuity spaces (to appear).Google Scholar
[10]Kopperman, R., Length spaces (to appear).Google Scholar
[11]Kowalsky, H. J., Beiträge zur topologischen Algebra, Mathematische Nachrichten, vol. 11 (1954), pp. 143–185.CrossRefGoogle Scholar
[12]Nakano, T., On the locally bounded fields, Commentarii Mathematici Universitatis Sancti Pauli, vol. 9 (1961), pp. 77–85.Google Scholar