R&E 30

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Research and Exposition in Mathematics -- Volume 30

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Ivan Chajda, Radomír Halaš, Jan Kühr

Semilattice Structures

viii+228 pages, soft cover, ISBN 978-3-88538-230-0, EUR 28.00, 2007

Connections between logic and lattices were already mentioned by Garrett Birkhoff in his monograph "Lattice Theory" published in 1940 and a number of books appeared since then on this topic discussing semilattices and semilattice structures however only marginally.

The aim of our monograph is to remedy this situation by concentrating on semilattices and semilattice structures exclusively. We also discuss implication logics, but focus on the collection of descriptions and properties of the corresponding algebraic structures. We present many known and new results, in particular on semilattices equipped with supplementary operations such as for example pseudocomplementation or relative pseudocomplementation and their generalizations.

We believe that this book can be of considerable interest for algebraists working on semilattice structures or algebras related to logic as well as for logicians. We suppose that the book can initiate a further development of the topic and that it can in particular be useful for mathematicians starting to work in semilattice structures.

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