Supersimple theories
Tóm tắt
We prove elimination of hyperimaginaries in supersimple theories. This means that if an equivalence relation on the set of realisations of a complete type (in a supersimple theory) is defined by a possibly infinite conjunction of first order formulas, then it is the intersection of definable equivalence relations.
Từ khóa
Tài liệu tham khảo
[1] S. Buechler, Lascar strong types in some simple theories, Journal of Symbolic Logic, 64(1999), 817-824.
[2] S. Buechler, Canonical bases in some supersimple theories, preprint 1998.
[3] B. Hart and A. Pillay, A note on canonical bases, preprint 1998.
[4] B. Hart, B. Kim and A. Pillay, Coordinatization and canonical bases, Journal of Symbolic Logic, 65(2000), 293-309.
[5] E. Hrushovski, Pseudofinite fields and related structures, preprint 1991.
[6] E. Hrushovski, Simplicity and the Lascar group, preprint 1997.
[7] B. Kim, Simple first order theories, Ph.D. thesis, University of Notre Dame, 1996.
Kim, Byunghan, 1998, Forking in simple unstable theories, J. London Math. Soc. (2), 57, 257, 10.1112/S0024610798005985
Kim, Byunghan, 1997, Recent results on simple first order theories, 202, 10.1017/CBO9780511629174.014
Kim, Byunghan, 1998, A note on Lascar strong types in simple theories, J. Symbolic Logic, 63, 926, 10.2307/2586720
[11] B. Kim, Simplicity and stability in there, to appear in Journal of Symbolic Logic.
[13] D. Lascar and A. Pillay, Hyperimaginaries and automorphism groups, to appear in Journal of Symbolic Logic.
[15] Z. Shami, A natural finite equivalence relation definable in low theories, to appear.