1. A GEOMETRIC INTRODUCTION TO FORKING AND THORN-FORKING.
- Author
-
ADLER, HANS
- Subjects
- *
AXIOMS , *AXIOMATIC set theory , *FIRST-order logic , *MATHEMATICAL logic , *LATTICE theory - Abstract
A ternary relation ${\hbox to 0pt{\hss\mid$\hss}\limits_\hbox to 0pt{\hss\smile$\hss}}$ between subsets of the big model of a complete first-order theory T is called an independence relation if it satisfies a certain set of axioms. The primary example is forking in a simple theory, but o-minimal theories are also known to have an interesting independence relation. Our approach in this paper is to treat independence relations as mathematical objects worth studying. The main application is a better understanding of thorn-forking, which turns out to be closely related to modular pairs in the lattice of algebraically closed sets. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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