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Independence, dimension and continuity in non-forking frames

Published online by Cambridge University Press:  12 March 2014

Adi Jarden  and
Alon Sitton
Adi Jarden
Affiliation:
Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, Israeland Department of Mathematics, Bar-Ilan University, Ramatgan 52900, Israel, E-mail:jardenadi@gmail.com
Alon Sitton
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem, Israel, E-mail:alonsitton@gmail.com
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Abstract

The notion J is independent in (M, M0, N) was established by Shelah, for an AEC (abstract elementary class) which is stable in some cardinal λ and has a non-forking relation, satisfying the good λ-frame axioms and some additional hypotheses. Shelah uses independence to define dimension.

Here, we show the connection between the continuity property and dimension: if a non-forking satisfies natural conditions and the continuity property, then the dimension is well-behaved.

As a corollary, we weaken the stability hypothesis and two additional hypotheses, that appear in Shelah's theorem.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013 , pp. 602 - 632
Copyright
Copyright © Association for Symbolic Logic 2013

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