Abstract
In this paper we will prove that ifF is a filter of a free Boolean algebra such that the minimal cardinality of the set of generators ofF is an uncountable regular cardinal or a singular cardinal with uncountable cofinality thenF is freely generated.
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References
Balcar, B., Franek F., 1982, ‘Independent families in complete Boolean algebras’, TAMS, 274, 607–618.
Gratzer, G., 1967,Universal algebra, Princeton.
Grygiel, J., 1988, ‘Absolute independence in atomless algebras, Universal and Applied Algebra’, inProceedings of the V Universal Algebra Symposium edited by K. Hałowska, B. Stawski, World Scientific.
Grygiel, J., 1990, ‘Absolutely independent sets of generators of filters in Booolean algebras’,Reports on Mathematical Logic 24, 25–35.
Koppelberg, S., 1989, ‘Free Constructions’, inHandbook of Boolean algebras, edited by Monk J.D, Bonnet R., North Holland.
Monk, J. D., 1983, ‘Independence in Boolean algebras’,Periodica Mathematica Hungarica—/14, 269–308.
Reznikoff, I., ‘Free axiomatizations in classical logic’, preprint.
Reznikoff I., 1965, ‘Tout ensemble de formules de la logique classique est équivalent á un ensemble indépendant’,Compets Rendus Hebdomadiares Acad. Sci. Paris 260, 2385–2388.
Reznikoff I., 1993, private correspondence.
Shelah S., 1980, ‘Remarks on Boolean algebras’,Alg. Univ. 11, 77–89.
Sikorski R., 1960,Boolean algebras, Berlin, Gottingen, Heidelberg.
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Grygiel, J. Freely generated filters in free Boolean algebras. Stud Logica 54, 139–147 (1995). https://doi.org/10.1007/BF01063149
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DOI: https://doi.org/10.1007/BF01063149