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In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k−1)-ary fragment of partial fixed point logic by all (2k−1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are...
LetL be one of the intuitionistic modal logics considered in  (or one of its extensions) and letM
L be the “algebraic semantics” ofL. In this paper we will extend toL the equivalence, proved in the classical case (see ), among he weak Craig interpolation theorem, the Robinson theorem and...
A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the corresponding negation (Gödel's negation). Algebraic proof methods are used. The meaning for fuzzy...
It is possible to completely characterize which countable models generated by 0# exist inL. This in turn has applications in the study of analytic equivalence relations; for instance, ifE is∑
and every invariant∑
(0#) set isΔ
, thenE has at most ℵ0 many equivalence classes.
In this paper I prove the following theorems which are the converses of some results of Judah and Laver (1983) and of Judah and Marshall (1993).
-IfKM+ATW is not an extension by definition ofKM (and the model involved is well founded), then the existence of two inaccessible cardinals is...
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