No CrossRef data available.
Article contents
Positive ∑ operations on ordinals and normal filters on greatly mahlo cardinals
Published online by Cambridge University Press: 12 March 2014
Abstract
If ℱ is a normal filter on a regular uncountable cardinal κ, let ║f║ be the ℱ-norm of an ordinal function f. We introduce the class of positive ordinal operations and prove that if F is a positive operation then ║F(f)║ ≥ F(║f║). For each η < κ+ let fη be the canonical ηth function. We show that if F is a ∑ operation then F(fη) = fF(η).
As an application we show that if κ is greatly Mahlo then there are normal filters on κ of order greater than κ+.
- Type
- Research Article
- Information
- Copyright
- Copyright © Association for Symbolic Logic 1989