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Weakly representable atom structures that are not strongly representable, with an application to first order logic
Author(s) -
Ahmed Tarek Sayed
Publication year - 2008
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.200710038
Subject(s) - mathematics , atom (system on chip) , set (abstract data type) , representation (politics) , order (exchange) , pure mathematics , binary number , first order logic , basis (linear algebra) , combinatorics , algebra over a field , discrete mathematics , arithmetic , computer science , geometry , finance , politics , political science , embedded system , law , economics , programming language
Let n > 2. A weakly representable relation algebra that is not strongly representable is constructed. It is proved that the set of all n by n basic matrices forms a cylindric basis that is also a weakly but not a strongly representable atom structure. This gives an example of a binary generated atomic representable cylindric algebra with no complete representation. An application to first order logic is given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)