Local Homogeneity

Journal of Symbolic Logic 69 (4):1243 - 1260 (2004)
We study the expansion of stable structures by adding predicates for arbitrary subsets. Generalizing work of Poizat-Bouscaren on the one hand and Baldwin-Benedikt-Casanovas-Ziegler on the other we provide a sufficient condition (Theorem 4.7) for such an expansion to be stable. This generalization weakens the original definitions in two ways: dealing with arbitrary subsets rather than just submodels and removing the 'small' or 'belles paires' hypothesis. We use this generalization to characterize in terms of pairs, the 'triviality' of the geometry on a strongly minimal set (Theorem 2.5). Call a set A benign if any type over A in the expanded language is determined by its restriction to the base language. We characterize the notion of benign as a kind of local homogenity (Theorem 1.7). Answering a question of [8] we characterize the property that M has the finite cover property over A (Theorem 3.9)
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1102022221
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,086
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Pseudo-Finite Homogeneïty and Saturation.Jörg Flum & Martin Ziegler - 1999 - Journal of Symbolic Logic 64 (4):1689-1699.
The Classification of Small Weakly Minimal Sets. II.Steven Buechler - 1988 - Journal of Symbolic Logic 53 (2):625-635.
Local Deductions Theorems.Janusz Czelakowski - 1986 - Studia Logica 45 (4):377 - 391.
Constructing Ω-Stable Structures: Rank 2 Fields.John T. Baldwin & Kitty Holland - 2000 - Journal of Symbolic Logic 65 (1):371-391.
Pseudoprojective Strongly Minimal Sets Are Locally Projective.Steven Buechler - 1991 - Journal of Symbolic Logic 56 (4):1184-1194.
S-Homogeneity and Automorphism Groups.Elisabeth Bouscaren & Michael C. Laskowski - 1993 - Journal of Symbolic Logic 58 (4):1302-1322.
Disjunctions in Closure Spaces.Andrzej W. Jankowski - 1985 - Studia Logica 44 (1):11 - 24.
Fine's Ways to Fail to Secure Local Realism.Soazig Le Bihan - 2009 - Studies in the History and Philosophy of Modern Physics 40 (2):142-150.
One Theorem of Zil'ber's on Strongly Minimal Sets.Steven Buechler - 1985 - Journal of Symbolic Logic 50 (4):1054-1061.
A Spector-Gandy Theorem for cPCd(A) Classes.Shaughan Lavine - 1992 - Journal of Symbolic Logic 57 (2):478 - 500.
Stretchings.O. Finkel & J. P. Ressayre - 1996 - Journal of Symbolic Logic 61 (2):563-585.


Added to PP index

Total views
18 ( #365,564 of 2,313,339 )

Recent downloads (6 months)
1 ( #535,322 of 2,313,339 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature