imaginary element

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

- Bruno Poizat,
*Une théorie de Galois imaginaire*, J. Symbolic Logic**48**(1984), no.4, 1151-1170, MR85e:03083, doi - wikipedia imaginary element
- Anand Pillay,
*Some remarks on definable equivalence relations in O-minimal structures*, J. Symbolic Logic**51**(1986), 709-714, MR87h:03046, doi - Jan Holly,
*Definable operations on sets and elimination of imaginaries*, Proc. Amer. Math. Soc.**117**(1993), no. 4, 1149–1157, MR93e:03052, doi, pdf - 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) - Saharon Shelah,
*Classification theory and the number of non-isomorphic models*, Studies in Logic and the Foundations of Mathematics**92**, North Holland, Amsterdam 1978

Revised on May 31, 2012 17:47:04
by Zoran Škoda
(193.51.104.33)