Studia Logica

, Volume 65, Issue 1, pp 91–112

Algebraic Characterizations of Various Beth Definability Properties

  • Eva Hoogland

DOI: 10.1023/A:1005295109904

Cite this article as:
Hoogland, E. Studia Logica (2000) 65: 91. doi:10.1023/A:1005295109904


In this paper it will be shown that the Beth definability property corresponds to surjectiveness of epimorphisms in abstract algebraic logic. This generalizes a result by I. Németi (cf. [11, Theorem 5.6.10]). Moreover, an equally general characterization of the weak Beth property will be given. This gives a solution to Problem 14 in [20]. Finally, the characterization of the projective Beth property for varieties of modal algebras by L. Maksimova (see [15]) will be shown to hold for the larger class of semantically algebraizable logics.

Abstract algebraic logic Beth definability property epimorphisms 

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Eva Hoogland
    • 1
  1. 1.ILLCUniversiteit van AmsterdamAmsterdamThe Netherlands

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