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The Beth Property in Algebraic Logic |
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| Authors: | W. J. Blok Eva Hoogland |
| Affiliation: | (1) Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851S Morgan Street, Chicago, Illinois 60607-7045, USA;(2) Netherlands Organisation for Scientific Research NWO, P.O. Box 93138, 2509 AC The Hague, The Netherlands |
| Abstract: | The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics. Dedicated to the memory of Willem Johannes Blok |
| Keywords: | Abstract algebraic logic equivalential logics algebraizable logics Beth definability property epimorphisms |
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