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A completeness theorem for higher order logics

Published online by Cambridge University Press:  12 March 2014

Gábor Sági
Gábor Sági*
Affiliation:
Alfréd Rényi Mathematical Institute, Hungarian Academy of Sciences, Budapest PF. 127, H-1364 Hungary, E-mail: sagi@math-inst.hu
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Abstract

Here we investigate the classes of representable directed cylindric algebras of dimension α introduced by Németi [12]. can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, “purely cylindric algebraic” proof for the following theorems of Németi: (i) is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain a strong representation theorem for if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of [11]) in some non-well-founded set theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 857 - 884
Copyright
Copyright © Association for Symbolic Logic 2000

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