Research and Exposition in Mathematics -- Volume 30
Ivan Chajda, Radomír Halaš, Jan Kühr
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.
List of Contents