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Recursive complexity of the Carnap first order modal logic C

✍ Scribed by Amélie Gheerbrant; Marcin Mostowski

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 134 KB
Volume: 52
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200410057

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✦ Synopsis

We consider first order modal logic C firstly defined by Carnap in "Meaning and Necessity" [1]. We prove elimination of nested modalities for this logic, which gives additionally the Skolem-Löwenheim theorem for C. We also evaluate the degree of unsolvability for C, by showing that it is exactly 0 . We compare this logic with the logics of Henkin quantifiers, Σ 1 1 logic, and SO. We also shortly discuss properties of the logic C in finite models.

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