## Journal of Symbolic Logic

### Independence, dimension and continuity in non-forking frames

#### Abstract

The notion $J$ is independent in $(M,M_0,N)$ was established by Shelah, for an AEC (abstract elementary class) which is stable in some cardinal $\lambda$ and has a non-forking relation, satisfying the good $\lambda$-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.

#### Article information

Source
J. Symbolic Logic, Volume 78, Issue 2 (2013), 602-632.

Dates
First available in Project Euclid: 15 May 2013

https://projecteuclid.org/euclid.jsl/1368627067

Digital Object Identifier
doi:10.2178/jsl.7802140

Mathematical Reviews number (MathSciNet)
MR3145198

Zentralblatt MATH identifier
1315.03048

#### Citation

Jarden, Adi; Sitton, Alon. Independence, dimension and continuity in non-forking frames. J. Symbolic Logic 78 (2013), no. 2, 602--632. doi:10.2178/jsl.7802140. https://projecteuclid.org/euclid.jsl/1368627067