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  1. A Completeness Theorem for Higher Order Logics.Gábor Sági - 2000 - Journal of Symbolic Logic 65 (2):857-884.
    Here we investigate the classes RCA $^\uparrow_\alpha$ of representable directed cylindric algebras of dimension α introduced by Nemeti[12]. RCA $^\uparrow_\alpha$ 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 Nemeti: (i) RCA $^\uparrow_\alpha$ is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain (...)
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  • Complexity of Equational Theory of Relational Algebras with Projection Elements.Szabolcs Mikulás, Ildikó Sain & Andras Simon - 1992 - Bulletin of the Section of Logic 21 (3):103-111.
    The class \ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of \ nor the first order theory of \ are decidable. Moreover, we show that the set of all equations valid in \ is exactly on the \ level. We consider the class \ of the relation algebra reducts of \ ’s, (...)
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  • Non-Standard Stochastics with a First Order Algebraization.Miklós Ferenczi - 2010 - Studia Logica 95 (3):345-354.
    Internal sets and the Boolean algebras of the collection of the internal sets are of central importance in non-standard analysis. Boolean algebras are the algebraization of propositional logic while the logic applied in non-standard analysis (in non-standard stochastics) is the first order or the higher order logic (type theory). We present here a first order logic algebraization for the collection of internal sets rather than the Boolean one. Further, we define an unusual probability on this algebraization.
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  • Complexity of Equational Theory of Relational Algebras with Standard Projection Elements.Szabolcs Mikulás, Ildikó Sain & András Simon - 2015 - Synthese 192 (7):2159-2182.
    The class $$\mathsf{TPA}$$ TPA of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $$\mathsf{TPA}$$ TPA nor the first order theory of $$\mathsf{TPA}$$ TPA are decidable. Moreover, we show that the set of all equations valid in $$\mathsf{TPA}$$ TPA is exactly on the $$\Pi ^1_1$$ Π 1 1 level. We consider the class $$\mathsf{TPA}^-$$ (...)
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