### A characterization of well-founced algebraic lattices

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G. Birkhoff, Lattice Theory, 3rd ed., A.M.S. Coll. Pub., vol. 25, American Mathematical Society, 1967.

I. Chakir, Chanes d'ideaux et dimension algebrique des treillis distributifs, Ph.D. thesis, Universite Claude-Bernard(Lyon1), 1992.

I. Chakir, The length of chains in modular lattices, Order 24 (2007), 227-247.

I. Chakir, Chains conditions in algebraic lattices, Ph.D. thesis, University Mohamed V, Faculty of Sciences, Rabat, May 2009, arXiv:1609.07167.

I. Chakir and M. Pouzet, The length of chains in distributive lattices, Abstracts of papers presented to the A.M.S. 92, 502-503, T-06-118.

I. Chakir and M. Pouzet, Infinite independent sets in distributive lattices, Algebra Universalis 53 (2005), no. 2, 211-225.

D. H. J. de Jongh and R. Parikh., Well-partial orderings and hierarchies, Indag. Math. (Proc) 80 (1977), no. 3, 195-207.

P. Erdos and A. Tarski, On families of mutually exclusive sets, Annals of Math. 44 (1943), 315-329.

R. Fraisse, Theory of Relations, North-Holland Publishing Co., Amsterdam, 2000.

F. Galvin, E. C. Milner, and M. Pouzet, Cardinal representations for closures and preclosures, Trans. Amer. Math. Soc. 328 (1991), 667-693.

G. Gratzer, General Lattice Theory, Birkhauser, Basel, 1998.

G. Higman, Ordering by divisibility in abstract algebras, Proc. London. Math. Soc. 2 (1952), no. 3, 326-336.

K. H. Hofmann, M. Mislove, and A. R. Stralka, The Pontryagin duality of compact 0-dimensional semilattices and its applications, Lecture Note in Mathematics, vol. 396, Springer-Verlag., 1974.

J. D. Lawson, M. Mislove, and H. A. Priestley, Infinite antichains in semilattices, Order 2 (1985), 275-290.

J. D. Lawson, M. Mislove, and H. A. Priestley, Ordered sets with no infinite antichains, Discrete Math. 63 (1987), 225-230.

J. D. Lawson, M. Mislove, and H. A. Priestley, Infinite antichains and duality theories, Houston Journal of Mathematics 14 (1988), no. 3, 423-441.

E. C. Milner and M. Pouzet, Combinatorics, Paul Erdos is Eighty, Report, 1993, pp. 277-299.

M. Mislove, When are order scattered and topologically scattered the same?, Annals of Discrete Math. 23 (1984), 61-80.

M. Pouzet and M. Sobrani, Ordinal invariants of an age, Tech. report, Universite Claude-Bernard (Lyon 1), August 2002.

M. Pouzet and N. Zaguia, Ordered sets with no chains of ideals of a given type, Order 1 (1984), 159-172.

F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1930), 264-286.

S. Shelah, Independence of strong partition relation for small cardinals, and the free subset problem, The Journal of Symbolic Logic 45 (1980), 505-509.

M. Sobrani, Sur les ages de relations et quelques aspects homologiques des constructions D+M, Ph.D. thesis, Universite S. M. Ben Abdallah-Fez, Fez, Morocco, 2002.

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