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Functorial maximal spectra

✍ Scribed by B. Banaschewski

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
159 KB
Volume
168
Category
Article
ISSN
0022-4049

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✦ Synopsis

Maximal spectra, of one kind or another, are usually not expected to be functorial, in notable contrast with the corresponding prime spectra, but there are cases in which the particular nature of the structures involved make them so. Here, we consider this in the context of compact normal frames, establishing the more fundamental functoriality of their saturation quotients which then readily implies that of their maximal spectrum, and showing this to be the common root of results concerning f-rings (

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INTR00ucT10~ 1.1. The real O# introduced by Solovay [9] has the following wellknown properties: (1) Let a be an ordinal such that L,[O"] is admissible; then a is a cardinal in the sense of L. (2) Conversely, let r be a real. Assume that every ordinal a, such that L,[r] is admissible, is a cardinal