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Definability problems in elementary topology

Published online by Cambridge University Press:  09 April 2009

Mariko Yasugi
Mariko Yasugi
Affiliation:
The Institute of Information ScienceUniversity of TsukubaSakuramura, IbarakiJapan305
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Abstract

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The elementary part of general topology is carried out in a system which is based on the arithmetically definable theory of the reals with definitions by definable induction (DDI), where a formal object is said to be definable if the quantifiers are restricted to the rationals, the names of the base members and the elements of the spaces.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 3 , June 1983 , pp. 399 - 420
Copyright
Copyright © Australian Mathematical Society 1983

References

Beeson, M. (1979), ‘Continuity in intuitionistic set theory’, Logic colloquium 78, Studies in logic and foundations of mathematics 97, edited by Boffa, M., Van Dalen, D., McAloon, K., pp. 1–52 (North-Holland Publ.Co., Amsterdam).Google Scholar
Bishop, E. (1979), Foundations of constructive analysis (McGraw-Hill Book Co., New York).Google Scholar
Bridges, D. S. (1979), Constructive functional analysis (Pitman, London).Google Scholar
Demuth, O. and Kučera, A. (1979), ‘Remarks on constructive mathematical analysis’ Logic colloquium 78, Studies in logic and the foundations of mathematics 97, edited by Boffa, M., Van Dalen, D., McAloon, K., pp. 81–129 (North-Holland Publ. Co., Amsterdam).Google Scholar
Feferman, S., (1979), ‘Constructive theories of functions and classes’, Logic colloquium 78, Studies in logic and the foundations of mathematics 97, edited by Boffa, M., Van Dalen, D., McAloon, K., pp. 159–224 (North-Holland Publ. Co., Amsterdam).Google Scholar
Friedman, H. (1977), ‘Set-theoretic foundations for constructive analysis’, Ann. Math. 105, 1–28.CrossRefGoogle Scholar
Myhill, J. (1975), ‘Constructive set theory’, J. Symbolic Logic 40, 347–383.CrossRefGoogle Scholar
Royden, H. L. (1968), Real analysis, second edition (Collier-Macmillan Limited, London).Google Scholar
Takeuti, G. (1975), Proof theory (North-Holland Publ.Co., Amsterdam).Google Scholar
Takeuti, G. (1978), Two applications of logic to mathematics (Iwanami Shoten and Princeton Univ. Press, Tokyo).Google Scholar
Troelstra, A. S. (1966), Intuitionistic general topology (Thesis, Amsterdam).Google Scholar
Troelstra, A. S. (1968), ‘One point compactifications of intuitionistic locally compact spaces’, Fund. Math. 62, 75–93.CrossRefGoogle Scholar
Yasugi, M. (1973), ‘Arithmetically definable analysis’, Proc. Res. Inst. Math. Sci. 180, 39–51.Google Scholar
Yasugi, M. (1981a), ‘The Hahn-Banach theorem and a restricted inductive definition’, Lecture Notes in Math. 891, pp. 359–394 (Springer-Verlag, Berlin).Google Scholar
Yasugi, M. (1981b), ‘Definability problems in metric spaces; a summary’, Proc. Res. Inst. Math. Sci. 441, 66–82.Google Scholar