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First order topology

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Rozprawy Matematyczne tom/nr w serii: 143 wydano: 1977
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CONTENTS

§ 1. Introduction.................................................................................................... 5
§ 2. Basic development............................................................................................... 8
§ 3. Some elementarily equivalent spaces............................................................. 11
§ 4. Elementary characterizations of some familiar spaces................................ 13
§ 5. First order properties of C(X).............................................................................. 16
§ 6. ℒ(X) and C(X) compared..................................................................................... 26
§ 7. Some results on undecidability.......................................................................... 28
§ 8. The class of topology lattices............................................................................. 32
§ 9. Some bounds on the Löwenheim number for topology lattices.................. 33
§10. Open questions................................................................................................... 36
References.................................................................................................................... 39
Słowa kluczowe
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Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 143
Liczba stron
40
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Opis fizyczny
Dissertationes Mathematicae, Tom CXLIII
Daty
wydano
1977
Twórcy
Bibliografia
  • [1] A. Adler, An application of elementary model theory to topological Boolean algebras, in Victoria Symposium on Nonstandard Analysis, Lecture Notes in Mathematics, vol. 369, Berlin 1974, pp. 1-4.
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  • [6] S. Feferman Infinitary properties, local functors and systems of ordinal functions, in Conference in Mathematical Logic, London 70, Lecture Notes in Mathematics, vol. 255, Berlin 1972, pp. 63-97.
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  • [9] P. Halmos, Lectures on Boolean Algebras, Berlin 1963.
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  • [13] A. MacIntyre, On the elementary theory of Banach algebras, Ann. Math. Logio 3 (1971), pp. 239-269.
  • [14] M. Makkai, A compactness result concerning direct products of models, Fund. Math. 57 (1965), pp. 313-325.
  • [15] S. Mazurkiewicz et W. Sierpiński, Contribution à la topologie des ensembles dénombrables, ibidem 1 (1920), pp. 17-27.
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  • [18] A. Mostowski, On direct products of theories, J. Symb. Logic 17 (1952), pp. 1-31.
  • [19] M. O. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc. 141 (1969), pp. 1-35.
  • [20] B. M. Robinson, Restricted set-theoretical definitions in arithmetic, Proc. Amer. Math. Soc. 9 (1958), pp. 238-242.
  • [21] H. Rogers, Jr., Theory of Recursive Functions and Effective Computability, New York 1967.
  • [22] W. Rudin, Homogeneity problems in the theory of Čech compactifications, Duke J. Math. 29 (1956), pp. 409-419.
  • [23] S. Shelah, The monadic theory of order, Ann. of Math. 102 (1975), pp. 379-419.
  • [24] J. R. Shoenfield, Mathematical Logic, Reading, Mass. 1967.
  • [25] J. Silver, A large cardinal in the constructive universe, Fund. Math. 49 (1970), pp. 93-100.
  • [26] T. Skolem, Untersuchungen über die Axiome des Kassenkalküls und über "Produkctations und Summationsprobleme", welche gewisse Klassen von Aussagen betreffen, Skrifter utgit av Videnskapsselskapet i Kristiana, I. Klasse, no. 3 , Oslo 1919.
  • [27] A. Swett, Topological spaces elementarily equivalent to the line, Notices Amer. Math. Soc. 22, February 1975, Abstract 75T-E23, p. A-328.
  • [28] A. Tarski, A Decision Method for Elementary Algebra and Geometry, California 1948.
  • [29] R. L. Wilder, Topology of manifolds, A. M. S. Colloquium Publication 32 (1949), New York.
  • [30] Z. Frolik, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), pp. 87-91.
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