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.
@article{bwmeta1.element.bwnjournal-article-fmv151i1p1bwm, author = {Saharon Shelah}, title = {On Monk's questions}, journal = {Fundamenta Mathematicae}, volume = {149}, year = {1996}, pages = {1-19}, zbl = {0859.03025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv151i1p1bwm} }
Shelah, Saharon. On Monk’s questions. Fundamenta Mathematicae, Tome 149 (1996) pp. 1-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv151i1p1bwm/
[00000] [CK] C. C. Chang and H. J. Keisler, Model Theory, Stud. Logic Found. Math. 73, North-Holland, Amsterdam, 1973.
[00001] [KpSh 415] S. Koppelberg and S. Shelah, Densities of ultraproducts of Boolean algebras, Canad. J. Math. 47 (1995), 132-145. | Zbl 0827.06008
[00002] [M] D. Monk, Cardinal functions of Boolean algebras, circulated notes. | Zbl 0557.06009
[00003] [P] D. Peterson, Cardinal functions on ultraproducts of Boolean algebras, J. Symbolic Logic, to appear. | Zbl 0883.03032
[00004] [Sh:92] S. Shelah, Remarks on Boolean algebras, Algebra Universalis 11 (1980), 77-89.
[00005] [Sh 355] S. Shelah, has a Jonsson algebra, in: Cardinal Arithmetic, Oxford Logic Guides 29, Chapter II, Oxford Univ. Press, 1994, 34-116.
[00006] [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. | Zbl 0844.03028
[00007] [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math., to appear.
[00008] [Sh 315] S. Shelah, PCF and infinite free subsets, Arch. Math. Logic, to appear.
[00009] [Sh:g] S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Oxford Univ. Press, 1994.