imaginary element

The category of definable sets and definable functions for a fixed language LL (or more generally, for an LL-theory TT) does not have finite colimits. Given a 1-st order language LL, and a theory TT in LL, we say that TT admits/has elimination of imaginaries if it one can take the quotients of definable sets by equivalence relations.

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  • wikipedia imaginary element
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  • Ehud Hrushovski, Groupoids, imaginaries and internal covers, arxiv/math.LO/0603413; On finite imaginaries, arxiv/0902.0842
  • D. Haskell, E. Hrushovski, H.D.Macpherson, Definable sets in algebraically closed valued fields: elimination of imaginaries, J. reine und angewandte Mathematik 597 (2006)
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Revised on May 31, 2012 17:47:04 by Zoran Škoda (