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Some Results on the Structure of the ϕ-Spectrum

✍ Scribed by Jerrold M. Gold

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
270 KB
Volume
26
Category
Article
ISSN
0044-3050

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✦ Synopsis

SOME RESULTS ON THE STRUCTURE O F THE y-SPECTRUM

by JERROLD M. GOLD in Northridge, California (U.S.A.)

81. Preliminaries and definitions

In this paper we prove a result about the relationship between measurable and definable cardinals and also a result on the spectrum of infinite cardinals. In a previous article [I], we introduced the notion of a definable cardinal. Definable cardinals are ones which do not posses a certain Lowenheim-Skolem type reflection property. I n [l]

we showed that the "small " infinite cardinals, K,, 2:, n €0, are all definable. Now we prove that ' ( large " measurable cardinals do indeed possess this reflection property, i.e. measurable cardinals are not definable.

L will denote a countable language. If the relation symbol P doesn't occur in L, we shall denote by L u (P) the obvious extension of L which includes P. Models for L will be denoted by the capital German letters a, 23.

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