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Tytuł książki

Boolean powers as algebras of continuous functions

Autorzy

Bernhard Banaschewski Evelyn Nelson

Seria

Rozprawy Matematyczne tom/nr w serii: 179 wydano: 1980

Zawartość

Pełne teksty:
rm179_01.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS

Introduction................................................. 5
1. Fundamentals................................................ 7
2. Functorial aspects......................................... 11
3. Congruences.................................................. 18
4. Exponent laws................................................ 28
5. Finite A............................................................. 34
6. Boolean ultrapowers..................................... 37
7. Elementary properties.................................. 45
Concluding remarks.......................................... 49
References.......................................................... 50

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 179

Liczba stron

51

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CLXXIX

Daty

wydano
1980

Twórcy

autor
Bernhard Banaschewski
  • McMaster University, Hamilton, Ontario
autor
Evelyn Nelson
  • McMaster University, Hamilton, Ontario

Bibliografia

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  • [3] B. Banaschewski, Equational compactness in universal algebra, Lecture notes, Prague 1973.
  • [4] B. Banaschewski, Equationally compact extensions of algebras, Alg. Univ. 4 (1974), pp. 20-35.
  • [5] B. Banaschewski, and G. Bruns, Categorical characterization of the MacNeille completion, Archiv Math. 18 (1967), pp. 369-377.
  • [6] B. Banaschewski, and H. Herrlich, Subcategories defined by implications, Houston J. Math. 2 (1976), pp. 149-171.
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  • [8] P. Bankston, Baire category and uniform boundedness for topological ultraproducts, manuscript, McMaster, 1976.
  • [9] B. Brainerd and J. Lambek, On the ring of quotients of a Boolean ring, Canad. Math. Bull. 2 (1959), pp. 25-29.
  • [10] N. Bourbaki, General topology. Part 2, Addison-Wesley.
  • [11] S. Bulman-Fleming and H. Werner, Equational compactness in quasi-primal varieties, Notices Amer. Math. Soc. 22 (1975), pp. A-448.
  • [12] S. Burris, Boolean powers, Alg, Univ. 5 (1975), pp. 341-360.
  • [13] S. Burris, and E. Jeffers, On the simplicity and subdirect irreducibility of Boolean ultrapowers. Manuscript, University or Waterloo, 1974.
  • [14] S. Burris, and H. Werner, Sheaf constructions and their elementary properties, manuscript, 1976.
  • [15] C. C. Chang and H. J. Keisler, Model theory. North Holland 1974.
  • [16] S. D. Comer, Elementary properties of structures of sections, Bol. Soc. Math. Mexicana.
  • [17] A. Daigneault, Boolean powers in algebraic logic, Zeit. Math. Logik und Grund. Math. 17 (1971), pp. 411-420.
  • [18] B. Davey, Free products of bounded distributive lattices, Alg. Univ, 4 (1974), pp. 106-107.
  • [19] B. Davey, Weak injectivity and congruence extension in congruence distributive equational classes, manuscript, La Trobe Univ., Bundoora, Victoria, Australia.
  • [20] A. Day, Injectivity in congruence distributive equational classes, Canad. J. Math. 24 (1974), pp. 209-220.
  • [21] S. Feferman and R. L. Vaught, The first order properties of products of algebraic systems, Fund Math. 47 (1969), pp. 57-103.
  • [22] J. Flachsmeyer, Dedekind-MacNeille extensions of Boolean algebras and of vector lattices of continuous functions and their structure spaces. Unpublished, manuscript.
  • [23] A. L. Foster, Generalized Boolean theory of universal algebra, I and II, Math. Z. 58 (1953), pp. 306-336 and 59 (1953), pp. 191-199.
  • [24] L. Gillman and M. Jerison, Rings of continuous functions. Van Nostrand, 1960.
  • [25] I. Glicksberg, Stone-Čech compactifications of products, Trans. Amer. Math. Soc. 90 (1959), pp. 369-382.
  • [26] H. Gonshor, On $GL_n$(B) where B is a Boolean ring, Canad. Math. Bull. 18 (1975), pp. 209-215.
  • [27] M. Gould and G. Gratzer, Boolean extensions and normal subdirect powers of finite universal algebras, Math. Z. 99 (1967), pp. 16-25.
  • [28] G. Gratzer, Universal algebra, Van Nostrand, 1968.
  • [29] P. R. Halmos, Lectures on Boolean algebras, Van Nostrand, 1963.
  • [30] D. Higgs, private communication.
  • [31] T. K. Hu, Stone duality for primal algebra theory, Math. Z. 110 (1969), pp. 180-198,
  • [32] T. K. Hu, On the topological duality for primal algebra theory, Alg. Univ. 1 (1971), pp. 152-154.
  • [33] B. Jónnson, review of: A. L. Foster, Functional completeness in the small algebraic structure theorems and identities, Math. Ann. 143 (1961), pp. 29-58. M. R. 23 (1962), A84.
  • [34] B. Jónnson and P. Olin, Elementary equivalence and relatively free products of lattices, manuscript.
  • [35] G. Kreisel and J. Krivine, Elements of mathematical logic, North Holland, 1967.
  • [36] S. MacLane, Categories for the working mathematician, Springer, 1971.
  • [37] R. Magari, Una dimostrazione del fatto che ogni varieta ammette algebre semplici, Ann. Univ. Ferrara (N. S.) 14 (1969), pp. 1-4.
  • [38] R. Mansfield, Boolean ultrapowers, Ann. Math. Logic 2 (1971), pp. 297-323.
  • [39] J. Mycielski, Some compactifications of general algebras, Colloq. Math. 13 (1964), pp. 1-9.
  • [40] A, Pixley, Functionally complete algebras, generating distributive and permutable classes, Math. Z. 114 (1970), pp. 361-372.
  • [41] P. Olin, Free products and elementary types of Boolean algebra, manuscript, York University, 1975.
  • [42] R. W. Quackenbush, Free products of bounded distributive lattices, Alg. Univ. 2 (1972), pp. 393-395.
  • [43] R. W. Quackenbush, Structure theory for equational classes generated by quasi-primal algebras, Trans. Amer. Math. Soc. 187 (1974), pp. 127-145.
  • [44] P. Ribenboim, Boolean powers. Fund. Math. 65 (1969), pp. 243-268.
  • [45] G. Sacks, Saturated model theory, W. A. Benjamin, 1972.
  • [46] R, Sikorski, Boolean algebras, Springer, 1964.
  • [47] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), pp. 375-481.
  • [48] W. Taylor, Some constructions of compact algebras, Ann. Math. Logic 3 (1971), pp. 395-437.
  • [49] W. Taylor, Residually small varieties, Alg. Univ. 2 (1972), pp. 33-53.
  • [50] W. Taylor, Pure compactifications in quasi-primal varieties, Canad J. Math. 28 (1976), pp. 50-62.
  • [51] H. Volger, The Feferman-Vaught theorem revisited, Colloq. Math, (to appear).
  • [52] J. Waszkiewicz and B. Węglorz, Some models of theories of reduced powers, Bull. Acad. Pol on. Sci. 16 (1968), pp. 683-685.
  • [53] B. Węglorz, Equationally compact algebras I, Fund. Math. 59 (1966), pp. 289-298.
  • [54] B. Węglorz, Some remarks on reduced powers (abstract), J. S. L. 39 (1974), p. 387.
  • [55] B. Węglorz, Substructures of reduced powers, Fund. Math. 89 (1975), pp. 191-197.
  • [56] H. Werner, Varieties generated by quasi-primal algebras have decidable theories (preprint 1974).

Języki publikacji

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Identyfikator YADDA

bwmeta1.element.zamlynska-0c151023-0f1e-4ef7-9dbf-016fbf292ca2

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ISBN
83-01-01115-7
ISSN
0012-3862

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DML-PL
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