Boolean constructions of independent sets of generators for filters

• Autorzy: Grygiel J.
• Języki publikacji: EN

Abstrakty

EN

Let F be a filter in a Boolean algebra. We consider the problem if it possible to construct an independent set of generators for F from any its set of generators. It turns out that the answer to this question depends on the minimal cardinality of the set of generators of F.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2001
• Tom: No. 35
• Strony: 75--85

Twórcy

autor

Grygiel J.

• Wyższa Szkoła Pedagogiczna Instytut Matematyki Al. Armii Krajowej 13/15 42-200 Częstochowa

Bibliografia

• [1] B. Balcar, F. Franek, Independent families in complete Boolean algebras, TAMS 274: 607–618, 1982.
• [2] J. Grygiel, Absolutely independent sets of generators of filters in Boolean algebras, Reports on Mathematical Logic 24: 25–35, 1990.
• [3] J. Grygiel, Freely generated filters in free Boolean algebras, Studia Logica 54: 139–147, 1995.
• [4] S. Koppelberg, Free Constructions, in Handbook of Boolean algebras, edited by J.D. Monk , R. Bonnet, North Holland, 1989.
• [5] J. D. Monk, Independence in Boolean algebras, Periodica Mathematica Hungarica 14: 269–308, 1983.
• [6] R. Sikorski, Boolean algebras, Berlin, Gottingen, Heidelberg, 1960.