Reports on Mathematical Logic 

About: Reports on Mathematical Logic is an academic journal published by Wydawnictwo Uniwersytetu Jagiellońskiego. The journal publishes majorly in the area(s): Variety (universal algebra) & Intermediate logic. It has an ISSN identifier of 0137-2904. It is also open access. Over the lifetime, 226 publications have been published receiving 1313 citations.

Varieties of Tense Algebras.

Abstract: A b s t r a c t. The paper has two parts preceded by quite comprehensive preliminaries. In the first part it is shown that a subvariety of the variety T of all tense algebras is discriminator if and only if it is semisimple. The variety T turns out to be the join of an increasing chain of varieties D n , which are discriminator varieties. The argument carries over to all finite type varieties of boolean algebras with operators satisfying some term conditions. In the case of tense algebras, the varieties D n can be further characterised by certain natural conditions on Kripke frames. In the second part it is shown that the lattice of subvarieties of D 0 has two atoms, the lattice of subvarieties of D 1 has countably many atoms, and for n > 1, the lattice of subvarieties of D n has continuum atoms. The proof of the second of the above statements involves a rather detailed description of zero-generated simple algebras in D 1. Almost all the arguments are cast in algebraic form, but both parts begin with an outline describing their contents from the dual point of view of tense logics.

Embedding and interpolation for some paralogics. the propositional case.

Abstract: A b s t r a c t. We consider the very weak paracomplete and paraconsistent logics that are obtained by a straightforward weakening of Classical Logic, as well as some of their maximal extensions that are a fragment of Classical Logic. We prove (for the propositional case) that these logics may be faithfully embedded in Classical Logic (as well as in each other), and that the interpolation theorem obtains for them.

The equational definability of truth predicates

Abstract: By a ‘logic’ we mean here a substitution-invariant consequence relation on formulas over an algebraic signature. Propositional logics are obvious examples, but even first order logic can be re-formulated in this way. The notion of an ‘algebraizable’ logic was made precise in the 1980s, mainly by Blok and Pigozzi, who provided intrinsic characterizations of the logics that are indeed algebraizable. One of their characterizations yields a practical strategy for showing that a logic is inherently non-algebraizable. The meaning of ‘algebraizable’ decomposes into two parts. In a slogan,