On the existence of prime ideals in Boolean algebras

• Autorzy: Jörg Flum
• Języki publikacji: EN

Abstrakty

EN

Rasiowa and Sikorski [5] showed that in any Boolean algebra there is an ultrafilter preserving countably many given infima. In [3] we proved an extension of this fact and gave some applications. Here, besides further remarks, we present some of these results in a more general setting.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1999
• Tom: 46
• Numer: 1
• Strony: 119-123

Daty

wydano

1999

Twórcy

autor

Jörg Flum

• Mathematisches Institut, Universität Freiburg, Eckerstr. 1, 79104 Freiburg, Germany

Bibliografia

• [1] J. Barwise and Y. N. Moschovakis, Global inductive definability, Jour. Symb. Logic 43(1978), 521-534.
• [2] E. Casanovas and R. Farré, Omitting types in incomplete theories, Jour. Symb. Logic 41(1996), 236-245.
• [3] J. Flum, An extension of the lemma of Rasiowa and Sikorski, to appear.
• [4] S. Koppelberg, General theory of Boolean algebras, Volume I of D. Monk, editor, Handbook of Boolean algebras, North-Holland, 1989.
• [5] H. Rasiowa and R. Sikorski, A proof of the completeness theorem of Gödel, Fund. Math. 37(1950), 193-200.
• [6] C. Ryll-Nardzewski, On the categoricity in power ≤ ω, Bull. Acad. Pol. Sci. 7(1959), 545-548.