Geodesic
A Technique to Generate -Ary Free Lattices from Finitary Ones
Canadian journal of mathematics, Tome 37 (1985) no. 2, pp. 324-336

Voir la notice de l'article provenant de la source Cambridge University Press

Let be an infinite regular cardinal. A poset L is called an -lattice if and only if for all X L satisfying 0 < |X| < m, ∧ X and ∨ X exist.This paper is a part of a sequence of papers, [5], [6], [7], [8], developing the theory of -lattices. For a survey of some of these results, see [9].The -lattice is described in [6]; γ denotes the zero and γ′ the unit of . In particular, formulas for -joins and meets are given. (We repeat the essentials of this description in Section 4.)In [6] we proved the theorem stated below. Our proof was based on characterization of (the free -lattice on P) due to [1]; as a result, our proof was very computational. 
Grätzer, George; Kelly, David. A Technique to Generate -Ary Free Lattices from Finitary Ones. Canadian journal of mathematics, Tome 37 (1985) no. 2, pp. 324-336. doi: 10.4153/CJM-1985-020-4
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[1] 1. Crawley, P. and Dean, R. A., Free lattices with infinite operations. Trans. Amer. Math. Soc. 92 (1959), 35–47. Google Scholar

[2] 2. Funayama, N., Notes on lattice theory IV. On partial (semi-) lattices, Bull. Yamagata Univ. (Nat. Sei.) 2 (1953), 171–184. Google Scholar

[3] 3. Grätzer, G., Universal algebra, Second Edition (Springer Verlag, New York, Heidelberg, Berlin, 1979). Google Scholar

[4] 4. Grätzer, G., General lattice theory. Pure and Applied Mathematics Series, Academic Press, New York, N.Y.; Mathematische Reihe, Band 52, Birkhauser Verlag, Basel; Akademie Verlag, Berlin, 1978. (Russian translation: MIR Publishers, Moscow, 1982.) Google Scholar

[5] 5. Grätzer, G. and Kelly, D., Free m-products of lattices. I and II, Colloq. Math., to appear. Google Scholar

[6] 6. Grätzer, G. and Kelly, D., The free m-lattice on the poset H, ORDER I (1984), 47–65. Google Scholar

[7] 7. Grätzer, G. and Kelly, D., An embedding theorem for free m-lattices on slender posets. Google Scholar

[8] 8. Grätzer, G. and Kelly, D., A description of free m-lattices on slender posets. Google Scholar

[9] 9. Grätzer, G. and Kelly, D., The construction of some free m-lattices on posets, Orders: Descriptions and Roles (Proceedings of the 1982 conference on ordered sets and their applications), (North-Holland, Amsterdam, 1984), 103–118. Google Scholar

[10] 10. Rival, I. and Willer, R., Lattices freely generated by partially ordered sets: which can be “drawn“?, J. Reine. Angew. Math. 310 (1979), 56–80. Google Scholar

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