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A dependent theory with few indiscernibles

by: Itay Kaplan, Saharon Shelah
(7 Sep 2012)  Key: citeulike:11893269

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Abstract

We continue the work started in [<a href="/abs/1009.5420">arXiv:1009.5420</a>], and prove the following theorem: For every $θ$ there is a dependent theory $T$ of size $θ$ such that for all $κ$ and $δ$, $κ\to(δ)_T,1$ iff $κ\to(δ)_θ^<ω$. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.


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