## Journal of Symbolic Logic

### Applications of PCF Theory

Saharon Shelah

#### Abstract

We deal with several pcf problems: we characterize another version of exponentiation: maximal number of $\kappa$-branches in a tree with $\lambda$ nodes, deal with existence of independent sets in stable theories, possible cardinalities of ultraproducts and the depth of ultraproducts of Boolean Algebras. Also we give cardinal invariants for each $\lambda$ with a pcf restriction and investigate further T$_D$(f). The sections can be read independently, although there are some minor dependencies.

#### Article information

Source
J. Symbolic Logic, Volume 65, Issue 4 (2000), 1624-1674.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746255

Mathematical Reviews number (MathSciNet)
MR1812172

Zentralblatt MATH identifier
0981.03048

JSTOR