On Monk’s questions

• Autorzy: Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 03E35: Consistency and independence results
• 03G05: Boolean algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 151
• Numer: 1
• Strony: 1-19

Daty

wydano

1996

otrzymano

1994-02-02

poprawiono

1996-01-17

Twórcy

autor

Saharon Shelah

• Institute of Mathematics, The Hebrew University, Jerusalem, Israel,
• Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.

Bibliografia

• [CK] C. C. Chang and H. J. Keisler, Model Theory, Stud. Logic Found. Math. 73, North-Holland, Amsterdam, 1973.
• [KpSh 415] S. Koppelberg and S. Shelah, Densities of ultraproducts of Boolean algebras, Canad. J. Math. 47 (1995), 132-145.
• [M] D. Monk, Cardinal functions of Boolean algebras, circulated notes.
• [P] D. Peterson, Cardinal functions on ultraproducts of Boolean algebras, J. Symbolic Logic, to appear.
• [Sh:92] S. Shelah, Remarks on Boolean algebras, Algebra Universalis 11 (1980), 77-89.
• [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.
• [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.
• [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math., to appear.
• [Sh 315] S. Shelah, PCF and infinite free subsets, Arch. Math. Logic, to appear.
• [Sh:g] S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Oxford Univ. Press, 1994.