Galois Groups of First order Theories

We study the groups GalL(T) and GalKP(T), and the associated equivalence relations EL and EKP, attached to a first order theory T. An example is given where EL≠ EKP (a non G-compact theory). It is proved that EKP is the composition of EL and the closure of EL. Other examples are given showing this is best possible.

[1]  S. Shelah,et al.  Annals of Pure and Applied Logic , 1991 .

[2]  Greg Hjorth,et al.  New dichotomies for Borel equivalence relations , 1997, Bull. Symb. Log..

[3]  Anand Pillay,et al.  Simple Theories , 1997, Ann. Pure Appl. Log..

[4]  Ehud Hrushovski,et al.  Simplicity and the Lascar group , 1998 .

[5]  Daniel Lascar,et al.  On the category of models of a complete theory , 1982, Journal of Symbolic Logic.

[6]  Steven Buechler.  Supersimple theories , 1997 .

[7]  Byunghan Kim,et al.  A note on Lascar strong types in simple theories , 1996, Journal of Symbolic Logic.

[8]  Anand Pillay,et al.  Hyperimaginaries and automorphism groups , 2001, Journal of Symbolic Logic.