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Positive ∑ operations on ordinals and normal filters on greatly mahlo cardinals

Published online by Cambridge University Press:  12 March 2014

Thomas Jech
Thomas Jech*
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
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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
The Journal of Symbolic Logic , Volume 54 , Issue 1 , March 1989 , pp. 226 - 233
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

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