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On neat embeddings of cylindric algebras

✍ Scribed by Tarek Sayed Ahmed

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 77 KB
Volume: 55
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200810028

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✦ Synopsis

Abstract

We show that certain properties of dimension complemented cylindric algebras, concerning neat embeddings, do not generalize much further. Let α ≥ ω. There are non‐isomorphic representable cylindric algebras of dimension α each of which is a generating subreduct of the same β dimensional cylindric algebra. We also show that there exists a representable cylindric algebra 𝔄 of dimension α, such that 𝔄 is a generating subreduct of 𝔅 and 𝔅′, both in CA~α +ω~ , however 𝔅 and 𝔅′ are not isomorphic. This settle questions raised by Henkin, Monk and Tarski (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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