Weakly representable atom structures that are not strongly representable, with an application to first order logic | Zendy

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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)

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