Riesz spaces and the ultrafilter theorem, I

G. J. H. M. Buskes; A. C. M. Van Rooij

Compositio Mathematica (1992)

  • Volume: 83, Issue: 3, page 311-327
  • ISSN: 0010-437X

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Buskes, G. J. H. M., and Van Rooij, A. C. M.. "Riesz spaces and the ultrafilter theorem, I." Compositio Mathematica 83.3 (1992): 311-327. <http://eudml.org/doc/90171>.

@article{Buskes1992,
author = {Buskes, G. J. H. M., Van Rooij, A. C. M.},
journal = {Compositio Mathematica},
keywords = {axiom of choice; Kakutani representation theorem for order unit spaces; ultrafilter theorem; Lipecki-Luxemburg-Schep theorem; Hahn-Banach theorem for Riesz homomorphisms},
language = {eng},
number = {3},
pages = {311-327},
publisher = {Kluwer Academic Publishers},
title = {Riesz spaces and the ultrafilter theorem, I},
url = {http://eudml.org/doc/90171},
volume = {83},
year = {1992},
}

TY - JOUR
AU - Buskes, G. J. H. M.
AU - Van Rooij, A. C. M.
TI - Riesz spaces and the ultrafilter theorem, I
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 83
IS - 3
SP - 311
EP - 327
LA - eng
KW - axiom of choice; Kakutani representation theorem for order unit spaces; ultrafilter theorem; Lipecki-Luxemburg-Schep theorem; Hahn-Banach theorem for Riesz homomorphisms
UR - http://eudml.org/doc/90171
ER -

References

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  1. [1] Aliprantis, C.D., and Burkinshaw, O., Positive Operators, Academic Press, 1985. Zbl0608.47039MR809372
  2. [2] Bacsich, P.D., Extension of Boolean homomorphisms with bounding seminorms, J. Reine Angew. Math.253, 24-27 (1972). Zbl0254.06008MR300951
  3. [3] Balbes, R. and Dwinger, P., Distributive Lattices, Univ. of Missouri Press, 1974. Zbl0321.06012MR373985
  4. [4] Banaschewski, B., The power of the Ultrafilter Theorem, J. London Math. Soc. (2) 27, 193-202 (1983). Zbl0523.03037MR692524
  5. [4a] Bernau, S., Unique Representation of Archimedean lattice groups and normal Archimedean lattice rings, Proc. London Math. Soc.15, 599-631 (1965). Zbl0134.10802MR182661
  6. [5] Buskes, G. and van Rooij, A., Hahn-Banach for Riesz homomorphisms, Indag. Math.51, 25-34 (1989). Zbl0683.46007MR993676
  7. [6] Buskes, G. and van Rooij, A., Small Riesz spaces, Math. Proc. Cambridge Phil. Soc.105, 523-536 (1989). Zbl0683.46013MR985689
  8. [7] Buskes, G., De Pagter, B. and van Rooij, A., Functional calculus in Riesz spaces, preprint. Zbl0781.46008
  9. [8] Feldman, D. and Henriksen, M., f-rings, subdirect products of totally ordered rings and the Prime Ideal Theorem, Indag. Math.50, 121-126 (1988). Zbl0656.06017MR952510
  10. [9] Gleason, A.M., Projective topological spaces, Ill. J. Math.2, 482-489 (1958). Zbl0083.17401MR121775
  11. [10] Hodges, W., Krull implies Zorn, J. London Math. Soc. (2) 19, 285-287 (1979). Zbl0394.03045MR533327
  12. [11] Jech, T., The Axiom of Choice, North Holland Publ. Co., Amsterdam, 1973. Zbl0259.02051MR396271
  13. [12] Johnstone, P.T., Stone Spaces, Cambridge Studies in Advanced Mathematics, Cambridge Univ. Press, 1982. Zbl0499.54001MR698074
  14. [13] de Jonge, E. and van Rooij, A., Introduction to Riesz Spaces, Math. Centre Tracts78, Amsterdam, 1977. Zbl0421.46001MR473777
  15. [14] Kakutani, S., Concrete representation of abstract (M)-spaces, Ann. Math.42, 994-1024 (1941). Zbl0060.26604MR5778
  16. [15] Levy, A., Basic Set Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1979. Zbl0404.04001MR533962
  17. [16] Lipecki, Z., Extension of vector-lattice homomorphisms, Proc. Amer. Math. Soc.79, 247-248 (1980). Zbl0441.47046MR565348
  18. [17] Luxemburg, W.A.J., Reduced powers of the real number system and equivalents of the Hahn-Banach extension theorem, Caltech Technical Report no. 2, 1967. Zbl0181.40101
  19. [18] Luxemburg, W.A.J., Some aspects of the theory of Riesz spaces, The University of Arkansas Lecture Notes in Mathematics, Volume 4, 1979. Zbl0431.46003MR568706
  20. [19] Luxemburg, W.A.J., Two applications of the method of construction by ultrapowers to analysis, Bull. A.M.S. 68, 416-419 (1962). Zbl0109.00803MR140417
  21. [20] Luxemburg, W.A.J., Non-standard analysis, Lectures on A. Robinson's Theory of Infinitesimals and Infinitely Large Numbers, Caltech1962. MR491162
  22. [21] Luxemburg, W.A.J., A remark on Sikorski's extension theory for homomorphisms in the theory of Boolean algebras, Fund. Math.55, 239-247 (1964). Zbl0147.25601MR177924
  23. [22] Luxemburg, W.A.J. and Schep, A.R., An extension theorem for Riesz homomorphisms, Indag. Math.41, 145-154 (1979). Zbl0425.46006MR535562
  24. [23] Luxemburg, W.A.J. and Zaanen, A.C., Riesz spaces I, North-Holland Publishing Company, Amsterdam, London, 1971. Zbl0231.46014MR511676
  25. [24] Luxemburg, W.A.J., Concurrent binary relations and embedding theorems for partially ordered linear spaces, Proc. First Int. Symposium Ordered Algebraic Structures, Luminy- Marseilles1984, Copyright Heldermann VerlagBerlin, 223-229 (1986). Zbl0625.06008MR891464
  26. [25] Luxemburg, W.A.J., A note on a paper by Feldman and Henriksen, Indag. Math.50, 127-130 (1988). Zbl0656.06018MR952511
  27. [26] Monteiro, A., Généralisation d'un théorème de R. Sikorski sur les algèbres de Boole, Bull. Sc. Math.89, 65-74 (1965). Zbl0133.27203MR186595
  28. [27] De Pagter, B., f-algebras and orthomorphisms, thesis, Leiden (1981). 
  29. [28] Rubin, H., and Rubin, J.E., Equivalents of the axiom of choice II, North-Holland, 1985. Zbl0129.00601MR798475
  30. [29] Schaefer, H.H., Banach lattices and positive operators, Springer-Verlag, Berlin, Heidelberg, New York, 1974. Zbl0296.47023MR423039
  31. [30] Schmidt, G.C., Extension of lattice homomorphisms, J. London Math. Soc. (2) 8, 707-710 (1974). Zbl0288.46008MR350374
  32. [31] Semadeni, Z., Banach spaces of continuous functions I, P.W.N., Warszawa, 1971. Zbl0225.46030
  33. [32] Sikorski, R., Boolean algebras, Third Edition, Springer-Verlag, 1969. Zbl0191.31505MR126393
  34. [33] Zaanen, A.C., Riesz spaces II, North-Holland Publishing Company, 1983. Zbl0519.46001MR704021

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