Properties and Consequences of th-Independence

Abstract

We develop a new notion of independence suggested by Scanlon (th-independence). We prove that in a large class of theories (which includes all simple theories) this notion has many of the properties needed for an adequate geometric structure in these models. We also prove that this definition agrees with the usual independence notions in stable, supersimple and o-minimal theories. Finally, many of the proofs and results we get for th-independence when restricted to simple theories seem to show there is some connection between th-independence and the stable forking conjecture. In particular, we prove that in any simple theory where this conjecture holds, our definition agrees with the classic definition.