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Mutual definability does not imply definitional equivalence, a simple example

✍ Scribed by Hajnal Andréka; Judit X. Madarász; István Németi

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 129 KB
Volume: 51
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200410051

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✦ Synopsis

We give two theories, Th1 and Th2, which are explicitly definable over each other (i. e. the relation symbols of one theory are explicitly definable in the other, and vice versa), but are not definitionally equivalent. The languages of the two theories are disjoint.