Lindström’s Theorems

Speaker: Mihai Prunescu (University of Bucharest)

Abstract: Regular logic systems which are strictly stronger than the first order predicate calculus cannot satisfy in the same time Löwenheim-Skolem for statements and compacity (Lindström 1). Effectively presented such systems cannot satisfy in the same time Löwenheim-Skolem for statements and the condition that the set of generally valid sentences is recursively enumerable (Lindström 2). We sketch the proof that uses partial isomorphisms.

References:
[1] H.-D. Ebbinghaus, J. Flum, W. Thomas, Mathematical Logic. Second edition, Undergraduate Texts in Mathematics, Springer, 1996.