Compactness\(=JEP\) in any logic. (English) Zbl 0564.03034

Mundici, Daniele

Fundam. Math. 116, 99-108 (1983).

Assuming constructibility, \(\neg 0^{\#}\) or \(\neg L^{\mu}\), the author proves that any logic with Löwenheim’s property is compact if and only if it has the joint embedding property. In some logics, algebraic characterizations of Robinson’s consistency theorem and Craig’s interpolation theorem are also found by using embedding properties.

MSC:

03C95	Abstract model theory
03C40	Interpolation, preservation, definability

Keywords:

Löwenheim’s property; joint embedding property; Robinson’s consistency theorem; Craig’s interpolation theorem