On Neat Embeddings of Algebraisations of First Order Logic
نویسنده
چکیده
Let α be an infinite ordinal. There are non-isomorphic representable algebras of dimension α each of which is a generating subreduct of the same β dimensional algebra. Dually there exists a representable algebra A of dimension , α such that A is a generating subreduct of B and , B′ however, B and B′ 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.
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