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Polyadic and cylindric algebras of sentences
Author(s) -
Amer Mohamed,
Sayed Ahmed Tarek
Publication year - 2006
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200510039
Subject(s) - interpretation (philosophy) , completeness (order theory) , isomorphism (crystallography) , mathematics , class (philosophy) , embedding , order (exchange) , gödel's completeness theorem , pure mathematics , algebra over a field , discrete mathematics , linguistics , philosophy , chemistry , epistemology , computer science , artificial intelligence , mathematical analysis , organic chemistry , finance , crystal structure , economics
In this note we give an interpretation of cylindric algebras as algebras of sentences (rather than formulas) of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)