Riesz spaces and the ultrafilter theorem, I
Buskes, G. J. H. M. ; Van Rooij, A. C. M.
Compositio Mathematica, Tome 84 (1992), p. 311-327 / Harvested from Numdam
Publié le : 1992-01-01
@article{CM_1992__83_3_311_0,
     author = {Buskes, G. J. H. M. and van Rooij, Arnoud C. M.},
     title = {Riesz spaces and the ultrafilter theorem, I},
     journal = {Compositio Mathematica},
     volume = {84},
     year = {1992},
     pages = {311-327},
     mrnumber = {1175943},
     zbl = {0781.46009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1992__83_3_311_0}
}
Buskes, G. J. H. M.; Van Rooij, A. C. M. Riesz spaces and the ultrafilter theorem, I. Compositio Mathematica, Tome 84 (1992) pp. 311-327. http://gdmltest.u-ga.fr/item/CM_1992__83_3_311_0/

[1] Aliprantis, C.D., and Burkinshaw, O., Positive Operators, Academic Press, 1985. | MR 809372 | Zbl 0608.47039

[2] Bacsich, P.D., Extension of Boolean homomorphisms with bounding seminorms, J. Reine Angew. Math. 253, 24-27 (1972). | MR 300951 | Zbl 0254.06008

[3] Balbes, R. and Dwinger, P., Distributive Lattices, Univ. of Missouri Press, 1974. | MR 373985 | Zbl 0321.06012

[4] Banaschewski, B., The power of the Ultrafilter Theorem, J. London Math. Soc. (2) 27, 193-202 (1983). | MR 692524 | Zbl 0523.03037

[4a] Bernau, S., Unique Representation of Archimedean lattice groups and normal Archimedean lattice rings, Proc. London Math. Soc. 15, 599-631 (1965). | MR 182661 | Zbl 0134.10802

[5] Buskes, G. and Van Rooij, A., Hahn-Banach for Riesz homomorphisms, Indag. Math. 51, 25-34 (1989). | MR 993676 | Zbl 0683.46007

[6] Buskes, G. and Van Rooij, A., Small Riesz spaces, Math. Proc. Cambridge Phil. Soc. 105, 523-536 (1989). | MR 985689 | Zbl 0683.46013

[7] Buskes, G., De Pagter, B. and Van Rooij, A., Functional calculus in Riesz spaces, preprint.

[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). | MR 952510 | Zbl 0656.06017

[9] Gleason, A.M., Projective topological spaces, Ill. J. Math. 2, 482-489 (1958). | MR 121775 | Zbl 0083.17401

[10] Hodges, W., Krull implies Zorn, J. London Math. Soc. (2) 19, 285-287 (1979). | MR 533327 | Zbl 0394.03045

[11] Jech, T., The Axiom of Choice, North Holland Publ. Co., Amsterdam, 1973. | MR 396271 | Zbl 0259.02051

[12] Johnstone, P.T., Stone Spaces, Cambridge Studies in Advanced Mathematics, Cambridge Univ. Press, 1982. | MR 698074 | Zbl 0499.54001

[13] De Jonge, E. and Van Rooij, A., Introduction to Riesz Spaces, Math. Centre Tracts 78, Amsterdam, 1977. | MR 473777 | Zbl 0421.46001

[14] Kakutani, S., Concrete representation of abstract (M)-spaces, Ann. Math. 42, 994-1024 (1941). | MR 5778 | Zbl 0060.26604

[15] Levy, A., Basic Set Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1979. | MR 533962 | Zbl 0404.04001

[16] Lipecki, Z., Extension of vector-lattice homomorphisms, Proc. Amer. Math. Soc. 79, 247-248 (1980). | MR 565348 | Zbl 0441.47046

[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. | Zbl 0181.40101

[18] Luxemburg, W.A.J., Some aspects of the theory of Riesz spaces, The University of Arkansas Lecture Notes in Mathematics, Volume 4, 1979. | MR 568706 | Zbl 0431.46003

[19] Luxemburg, W.A.J., Two applications of the method of construction by ultrapowers to analysis, Bull. A.M.S. 68, 416-419 (1962). | MR 140417 | Zbl 0109.00803

[20] Luxemburg, W.A.J., Non-standard analysis, Lectures on A. Robinson's Theory of Infinitesimals and Infinitely Large Numbers, Caltech 1962. | MR 491162

[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). | MR 177924 | Zbl 0147.25601

[22] Luxemburg, W.A.J. and Schep, A.R., An extension theorem for Riesz homomorphisms, Indag. Math. 41, 145-154 (1979). | MR 535562 | Zbl 0425.46006

[23] Luxemburg, W.A.J. and Zaanen, A.C., Riesz spaces I, North-Holland Publishing Company, Amsterdam, London, 1971. | MR 511676 | Zbl 0231.46014

[24] Luxemburg, W.A.J., Concurrent binary relations and embedding theorems for partially ordered linear spaces, Proc. First Int. Symposium Ordered Algebraic Structures, Luminy- Marseilles 1984, Copyright Heldermann Verlag Berlin, 223-229 (1986). | MR 891464 | Zbl 0625.06008

[25] Luxemburg, W.A.J., A note on a paper by Feldman and Henriksen, Indag. Math. 50, 127-130 (1988). | MR 952511 | Zbl 0656.06018

[26] Monteiro, A., Généralisation d'un théorème de R. Sikorski sur les algèbres de Boole, Bull. Sc. Math. 89, 65-74 (1965). | MR 186595 | Zbl 0133.27203

[27] De Pagter, B., f-algebras and orthomorphisms, thesis, Leiden (1981).

[28] Rubin, H., and Rubin, J.E., Equivalents of the axiom of choice II, North-Holland, 1985. | MR 798475 | Zbl 0129.00601

[29] Schaefer, H.H., Banach lattices and positive operators, Springer-Verlag, Berlin, Heidelberg, New York, 1974. | MR 423039 | Zbl 0296.47023

[30] Schmidt, G.C., Extension of lattice homomorphisms, J. London Math. Soc. (2) 8, 707-710 (1974). | MR 350374 | Zbl 0288.46008

[31] Semadeni, Z., Banach spaces of continuous functions I, P.W.N., Warszawa, 1971. | Zbl 0225.46030

[32] Sikorski, R., Boolean algebras, Third Edition, Springer-Verlag, 1969. | MR 126393

[33] Zaanen, A.C., Riesz spaces II, North-Holland Publishing Company, 1983. | MR 704021 | Zbl 0519.46001