Small profinite structures

Newelski, Ludomir

doi:10.1090/S0002-9947-01-02854-9

Small profinite structures
HTML articles powered by AMS MathViewer

by Ludomir Newelski PDF

Trans. Amer. Math. Soc. 354 (2002), 925-943 Request permission

Abstract:

We propose a model-theoretic framework for investigating profinite structures. We prove that in many cases small profinite structures interpret infinite groups. This corresponds to results of Hrushovski and Peterzil on interpreting groups in locally modular stable and o-minimal structures.

References

Steven Buechler, Essential stability theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1996. MR 1416106, DOI 10.1007/978-3-642-80177-8
E. Bouscaren and E. Hrushovski, On one-based theories, J. Symbolic Logic 59 (1994), no. 2, 579–595. MR 1276634, DOI 10.2307/2275409
Ehud Hrushovski, Locally modular regular types, Classification theory (Chicago, IL, 1985) Lecture Notes in Math., vol. 1292, Springer, Berlin, 1987, pp. 132–164. MR 1033027, DOI 10.1007/BFb0082236
Ludomir Newelski, Meager forking, Ann. Pure Appl. Logic 70 (1994), no. 2, 141–175. MR 1321462, DOI 10.1016/0168-0072(94)90028-0
Ludomir Newelski, $\scr M$-gap conjecture and m-normal theories, Israel J. Math. 106 (1998), 285–311. MR 1656901, DOI 10.1007/BF02773473
L.Newelski, Geometry of $*$-finite types, J.Symb.Logic 64(1999), 1375-1395.
L.Newelski, m-normal theories, Fund.Math., accepted.
Ludomir Newelski, Meager forking and $m$-independence, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 1998, pp. 33–42. MR 1648054
L.Newelski, Small profinite groups, J.Symb. Logic, accepted.
Ya’acov Peterzil, Constructing a group-interval in o-minimal structures, J. Pure Appl. Algebra 94 (1994), no. 1, 85–100. MR 1277525, DOI 10.1016/0022-4049(94)90007-8