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ArticleOriginal scientific text

Title

On the existence of prime ideals in Boolean algebras

Authors 1

Affiliations

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

Abstract

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.

Bibliography

  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.
Banach Center Publications
1999/46/1
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Pages:
119-123
Main language of publication
English
Published
1999
Exact and natural sciences