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Logic Journal of IGPL Advance Access originally published online on June 6, 2007
Logic Journal of IGPL 2007 15(2):183-197; doi:10.1093/jigpal/jzm006
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On Cylindric Algebras Satisfying Merry-go-round Properties

Miklós Ferenczi 1

Budapest University of Technology and Economics Institute of Mathematics, Department of Algebra, H–1111, Budapest, Egry J. u. 1, Hungary E-mail: ferenczi{at}math.bme.hu


  Abstract

Three classes are introduced which are closely related to the class Formula included in the title. It is proven that the class Formula obtained from Formula by replacing axiom C4 by the commutativity of single substitutions can be considered as the abstract class in the Resek–Thompson theorem, thus it is representable by set algebras. Then the class Formula is defined and it is shown that the necessary and sufficient condition for neat embeddability of an algebra in CA{alpha} into Formula is the validity of the merry-go-round properties. Finally, the class Formula is introduced which class is a counterpart of Formula among the polyadic like algebras.

Key Words: Cylindric and quasi polyadic algebras • representation

Received for publication 30 January 2006.

1Supported by the OTKA grants T035192, T43242.


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