Volume no :1, Issue no: 2, June (2008)

ON NEAT EMBEDDINGS OF ALGEBRAISATIONS OF FIRST ORDER LOGIC

Author's: Tarek Sayed Ahmed
Pages: [113] - [125]
Received Date: June 13, 2009
Submitted by:

Abstract

Let be an infinite ordinal. There are non-isomorphic representable algebras of dimension each of which is a generating subreduct of the same dimensional algebra. Dually there exists a representable algebra of dimension such that is a generating subreduct of and however, and are not isomorphic. The above was proven to hold for infinite dimensional cylindric algebras (CA’s) in [3] answering questions raised by Henkin et al. In this paper, we investigate the analogous statements for algebraisations other than cylindric algebras. We show that Pinter\'s substitution algebras and Halmos’ quasi-polyadic algebras behave like CA’s, however, Halmos polyadic algebras do not.

Keywords

algebraic logic, neat reducts, super amalgamation.