A relative interpolation theorem for infinitary universal Horn logic and its applications

Archive for Mathematical Logic 45 (3):267-305 (2006)
  Copy   BIBTEX


In this paper we deal with infinitary universal Horn logic both with and without equality. First, we obtain a relative Lyndon-style interpolation theorem. Using this result, we prove a non-standard preservation theorem which contains, as a particular case, a Lyndon-style theorem on surjective homomorphisms in its Makkai-style formulation. Another consequence of the preservation theorem is a theorem on bimorphisms, which, in particular, provides a tool for immediate obtaining characterizations of infinitary universal Horn classes without equality from those with equality. From the theorem on surjective homomorphisms we also derive a non-standard Beth-style preservation theorem that yields a non-standard Beth-style definability theorem, according to which implicit definability of a relation symbol in an infinitary universal Horn theory implies its explicit definability by a conjunction of atomic formulas. We also apply our theorem on surjective homomorphisms, theorem on bimorphisms and definability theorem to algebraic logic for general propositional logic.



    Upload a copy of this work     Papers currently archived: 91,349

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library


Added to PP

18 (#808,169)

6 months
9 (#298,039)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Subquasivarieties of implicative locally-finite quasivarieties.Alexej P. Pynko - 2010 - Mathematical Logic Quarterly 56 (6):643-658.

Add more citations

References found in this work

The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Zum intuitionistischen aussagenkalkül.K. Gödel - 1932 - Anzeiger der Akademie der Wissenschaften in Wien 69:65--66.
Logic of antinomies.F. G. Asenjo & J. Tamburino - 1975 - Notre Dame Journal of Formal Logic 16 (1):17-44.

View all 10 references / Add more references