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THORN-FORKING AS LOCAL FORKING.
- Source :
-
Journal of Mathematical Logic . Jun2009, Vol. 9 Issue 1, p21-38. 18p. 1 Diagram. - Publication Year :
- 2009
-
Abstract
- We introduce the notion of a preindependence relation between subsets of the big model of a complete first-order theory, an abstraction of the properties which numerous concrete notions such as forking, dividing, thorn-forking, thorn-dividing, splitting or finite satisfiability share in all complete theories. We examine the relation between four additional axioms (extension, local character, full existence and symmetry) that one expects of a good notion of independence. We show that thorn-forking can be described in terms of local forking if we localize the number k in Kim's notion of "dividing with respect to k" (using Ben-Yaacov's "k-inconsistency witnesses") rather than the forking formulas. It follows that every theory with an M-symmetric lattice of algebraically closed sets (in Teq) is rosy, with a simple lattice theoretical interpretation of thorn-forking. [ABSTRACT FROM AUTHOR]
- Subjects :
- *AXIOMATIC set theory
*LATTICE theory
*MATHEMATICS
*AXIOMS
*ABSTRACT algebra
Subjects
Details
- Language :
- English
- ISSN :
- 02190613
- Volume :
- 9
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Logic
- Publication Type :
- Academic Journal
- Accession number :
- 52303902
- Full Text :
- https://doi.org/10.1142/S0219061309000823