Tree indiscernibilities, revisited

Details Tree indiscernibilities, revisited Tree indiscernibilities, revisited

2011-11-03

arxiv.org/abs/1111.0915v1

Mathematics

Logic

submitted

Scientific paper

We give definitions that distinguish between two notions of indiscernibility for a sequence $(a_\eta \mid \eta \in \W)$ that saw original use in \cite{sh78}, which we name \textit{$\s$-} and \textit{$\s\s$-indiscernibility}. We restate proofs for \citep[{App. 2.6, 2.7}]{sh78}, expanding on the details. Using these definitions and detailed proofs, we prove $\s$- and $\s\s$-indiscernible modeling theorems and give some applications of these theorems. In particular, these clarified notions of indiscernibility supply a correct and complete proof of the fact that a theory has the tree property (TP) iff it has either TP$_1$ or TP$_2$.

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