On Monk’s questions

Saharon Shelah

Fundamenta Mathematicae (1996)

  • Volume: 151, Issue: 1, page 1-19
  • ISSN: 0016-2736

Abstract

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We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.

How to cite

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Shelah, Saharon. "On Monk’s questions." Fundamenta Mathematicae 151.1 (1996): 1-19. <http://eudml.org/doc/212179>.

@article{Shelah1996,
abstract = {We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.},
author = {Shelah, Saharon},
journal = {Fundamenta Mathematicae},
keywords = {Boolean algebra; -character; regular cardinals; singular cardinals; ultraproduct},
language = {eng},
number = {1},
pages = {1-19},
title = {On Monk’s questions},
url = {http://eudml.org/doc/212179},
volume = {151},
year = {1996},
}

TY - JOUR
AU - Shelah, Saharon
TI - On Monk’s questions
JO - Fundamenta Mathematicae
PY - 1996
VL - 151
IS - 1
SP - 1
EP - 19
AB - We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.
LA - eng
KW - Boolean algebra; -character; regular cardinals; singular cardinals; ultraproduct
UR - http://eudml.org/doc/212179
ER -

References

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  1. [CK] C. C. Chang and H. J. Keisler, Model Theory, Stud. Logic Found. Math. 73, North-Holland, Amsterdam, 1973. 
  2. [KpSh 415] S. Koppelberg and S. Shelah, Densities of ultraproducts of Boolean algebras, Canad. J. Math. 47 (1995), 132-145. Zbl0827.06008
  3. [M] D. Monk, Cardinal functions of Boolean algebras, circulated notes. Zbl0557.06009
  4. [P] D. Peterson, Cardinal functions on ultraproducts of Boolean algebras, J. Symbolic Logic, to appear. Zbl0883.03032
  5. [Sh:92] S. Shelah, Remarks on Boolean algebras, Algebra Universalis 11 (1980), 77-89. 
  6. [Sh 355] S. Shelah, ℵ ω + 1 has a Jonsson algebra, in: Cardinal Arithmetic, Oxford Logic Guides 29, Chapter II, Oxford Univ. Press, 1994, 34-116. 
  7. [Sh 420] S. Shelah, Advances in cardinal arithmetic, in: Finite and Infinite Combinatorics in Sets and Logic, N. W. Sauer et al. (eds.), Kluwer Acad. Publ., 1993, 355-383. Zbl0844.03028
  8. [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math., to appear. 
  9. [Sh 315] S. Shelah, PCF and infinite free subsets, Arch. Math. Logic, to appear. 
  10. [Sh:g] S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Oxford Univ. Press, 1994. 

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