Riesz spaces and the ultrafilter theorem, I
Compositio Mathematica, Tome 83 (1992) no. 3, pp. 311-327. 
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Buskes, G. J. H. M.; Van Rooij, A. C. M. Riesz spaces and the ultrafilter theorem, I. Compositio Mathematica, Tome 83 (1992) no. 3, pp. 311-327. http://www.numdam.org/item/CM_1992__83_3_311_0/

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

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

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

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

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

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

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

[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 | Zbl

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

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

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

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

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

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

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

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

[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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

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

[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 | Zbl

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

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

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

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

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