We show that there is a restriction, or modification of the
finite-variable fragments of First Order Logic in which a weak
form of Craig’s Interpolation Theorem holds but a strong form of
this theorem does not hold. Translating these results into
Algebraic Logic we obtain a finitely axiomatizable subvariety of
finite dimensional Representable Cylindric Algebras that has the
Strong Amalgamation Property but does not have the
Superamalgamation Property. This settles a conjecture of
Pigozzi [12].
Publié le : 2006-03-14
Classification:
Craig Interpolation,
Strong Amalgamation,
Superamalgamation,
Varieties of Cylindric Algebras,
03C40,
03G15
@article{1140641164,
author = {S\'agi, G\'abor and Shelah, Saharon},
title = {On weak and strong interpolation in algebraic logics},
journal = {J. Symbolic Logic},
volume = {71},
number = {1},
year = {2006},
pages = { 104-118},
language = {en},
url = {http://dml.mathdoc.fr/item/1140641164}
}
Sági, Gábor; Shelah, Saharon. On weak and strong interpolation in algebraic logics. J. Symbolic Logic, Tome 71 (2006) no. 1, pp. 104-118. http://gdmltest.u-ga.fr/item/1140641164/