# On the existence of prime ideals in Boolean algebras

Banach Center Publications (1999)

- Volume: 46, Issue: 1, page 119-123
- ISSN: 0137-6934

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topFlum, Jörg. "On the existence of prime ideals in Boolean algebras." Banach Center Publications 46.1 (1999): 119-123. <http://eudml.org/doc/208916>.

@article{Flum1999,

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.},

author = {Flum, Jörg},

journal = {Banach Center Publications},

keywords = {Rasiowa-Sikorski lemma; prime ideals; Boolean algebra; ultrafilter},

language = {eng},

number = {1},

pages = {119-123},

title = {On the existence of prime ideals in Boolean algebras},

url = {http://eudml.org/doc/208916},

volume = {46},

year = {1999},

}

TY - JOUR

AU - Flum, Jörg

TI - On the existence of prime ideals in Boolean algebras

JO - Banach Center Publications

PY - 1999

VL - 46

IS - 1

SP - 119

EP - 123

AB - 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.

LA - eng

KW - Rasiowa-Sikorski lemma; prime ideals; Boolean algebra; ultrafilter

UR - http://eudml.org/doc/208916

ER -

## References

top- [1] J. Barwise and Y. N. Moschovakis, Global inductive definability, Jour. Symb. Logic 43(1978), 521-534. Zbl0395.03021
- [2] E. Casanovas and R. Farré, Omitting types in incomplete theories, Jour. Symb. Logic 41(1996), 236-245. Zbl0854.03025
- [3] J. Flum, An extension of the lemma of Rasiowa and Sikorski, to appear. Zbl0919.03048
- [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. Zbl0040.29303
- [6] C. Ryll-Nardzewski, On the categoricity in power ≤ ω, Bull. Acad. Pol. Sci. 7(1959), 545-548.

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