Source: J. Symbolic Logic
Volume 71, Issue 1
We develop a new notion of independence (þ-independence, read
“thorn”-independence) that arises from a family of ranks suggested
by Scanlon (þ-ranks). We prove that in a large class of theories
(including simple theories and o-minimal theories) this notion has
many of the properties needed for an adequate geometric structure.
We prove that þ-independence agrees with the usual independence
notions in stable, supersimple and o-minimal theories. Furthermore,
we give some evidence that the equivalence between forking and
þ-forking in simple theories might be closely related to one of the
main open conjectures in simplicity theory, the stable forking
conjecture. In particular, we prove that in any simple theory where
the stable forking conjecture holds, þ-independence and forking
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