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There exists an uncountable set of pretabular extensions of the relevant logic R and each logic of this set is generated by a variety of finite height. (English) Zbl 1161.03011

A propositional logic is called pretabular if it is not generated by a finite algebra but every proper extension is. As for such logics, the results by Maksimova are well-known; there exist exactly three pretabular extensions of the intuitionistic logic, and exactly five pretabular extensions of the modal logic S4. On the other hand, the only known pretabular extension of the relevant logic R was the logic RM shown by Dunn, who then proposed a problem to find other pretabular extensions of R. The main results of this paper described by the title, give an answer to the problem showing a sharp contrast to the Maksimova’s results.

MSC:

03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
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