Minimum-sized Infinite Partitions of Boolean Algebras

Mathematical Logic Quarterly 42 (1):537-550 (1996)
  Copy   BIBTEX

Abstract

For any Boolean Algebra A, let cmm be the smallest size of an infinite partition of unity in A. The relationship of this function to the 21 common functions described in Monk [4] is described, for the class of all Boolean algebras, and also for its most important subclasses. This description involves three main results: the existence of a rigid tree algebra in which cmm exceeds any preassigned number, a rigid interval algebra with that property, and the construction of an interval algebra in which every well-ordered chain has size less than cmm.

Categories

Add categories

Keywords

Reprint years

DOI

10.1002/malq.19960420142

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,571

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Minimum‐sized Infinite Partitions of Boolean Algebras.J. Donald Monk - 1996 - Mathematical Logic Quarterly 42 (1):537-550.
σ-short Boolean algebras.Makoto Takahashi & Yasuo Yoshinobu - 2003 - Mathematical Logic Quarterly 49 (6):543-549.
A Note on Boolean Algebras with Few Partitions Modulo some Filter.Markus Huberich - 1996 - Mathematical Logic Quarterly 42 (1):172-174.
Partition Complete Boolean Algebras and Almost Compact Cardinals.Peter Jipsen & Henry Rose - 1999 - Mathematical Logic Quarterly 45 (2):241-255.
Boolean algebras in ast.Klaus Schumacher - 1992 - Mathematical Logic Quarterly 38 (1):373-382.
Chains and antichains in interval algebras.M. Bekkali - 1994 - Journal of Symbolic Logic 59 (3):860-867.
Free nilpotent minimum algebras.Manuela Busaniche - 2006 - Mathematical Logic Quarterly 52 (3):219-236.
Hyper-Archimedean BL-algebras are MV-algebras.Esko Turunen - 2007 - Mathematical Logic Quarterly 53 (2):170-175.
More on cardinal invariants of Boolean algebras.Andrzej Rosłanowski & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):1-37.
Boolean deductive systems of BL-algebras.Esko Turunen - 2001 - Archive for Mathematical Logic 40 (6):467-473.
The spectrum of partitions of a Boolean algebra.J. Donald Monk - 2001 - Archive for Mathematical Logic 40 (4):243-254.
Boolean products of R0-algebras.Xiangnan Zhou & Qingguo Li - 2010 - Mathematical Logic Quarterly 56 (3):289-298.
P ≠ NP for all infinite Boolean algebras.Mihai Prunescu - 2003 - Mathematical Logic Quarterly 49 (2):210-213.
The number of openly generated Boolean algebras.Stefan Geschke & Saharon Shelah - 2008 - Journal of Symbolic Logic 73 (1):151-164.
Semi-Cohen Boolean algebras.Bohuslav Balcar, Thomas Jech & Jindřich Zapletal - 1997 - Annals of Pure and Applied Logic 87 (3):187-208.

Analytics

Added to PP
2017-02-17

Downloads
5 (#1,533,504)

6 months
2 (#1,192,610)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Continuum Cardinals Generalized to Boolean Algebras.J. Donald Monk - 2001 - Journal of Symbolic Logic 66 (4):1928-1958.
Special subalgebras of Boolean algebras.J. Donald Monk - 2010 - Mathematical Logic Quarterly 56 (2):148-158.

Add more citations

References found in this work

No references found.

Add more references