Mutual definability does not imply definitional equivalence, a simple example

Mutual definability does not imply definitional equivalence, a simple example

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. (© 2005 WILEY‐VCH Verlag GmbH &...

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Veröffentlicht in:Mathematical logic quarterly 2005-11, Vol.51 (6), p.591-597
Hauptverfasser: Andréka, Hajnal, Madarász, Judit X., Németi, István
Format: Artikel
Sprache:eng
Schlagworte:
definability theory
Model theory
Model theory, definability theory
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Zusammenfassung: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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.200410051