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Interpretable Groups, Stably Embedded Sets, and Vaughtian Pairs |
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| Authors: | Herwig, Bernhard Hrushovski, Ehud Macpherson, Dugald |
| Affiliation: | Am Gonsenheimer Spiess 18, 55122 Mainz, Germany, herwig{at}math.uni-freiburg.de Department of Pure Mathematics, University of Leeds Leeds LS2 9JT, h.d.macpherson{at}leeds.ac.uk Department of Mathematics, Hebrew University Jerusalem, Israel, ehud{at}math.huji.ac.il |
| Abstract: | The paper concerns sufficiently saturated structures M overa countable language with a unary predicate P. It is shown thatif P(M)is stably embedded and there are no Vaughtian pairs withrespect to P, then an infinite group is interpretable over M(in an infinitary sense of interpretable). Also,it is shown that if M is  -categorical, f:D P is a 0-definablemap with finite fibres, and P(M) is stably embedded but D isnot, then some infinite group is first-order interpretable overM. |
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