Submission date: 6 November 2011.

Abstract:

We give definitions that distinguish between two notions of indiscernibility for a sequence (a_\eta | \eta \in ^{ω>}ω) that saw original use in [6], which we name s- and ss-indiscernibility}. We restate proofs for App. 2.6, 2.7 of [6], expanding on the details. Using these definitions and detailed proofs, we prove s- and ss-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.

Mathematics Subject Classification: 03C45, 05C55, 05C05

Keywords and phrases:

Full text arXiv 1111.0915: pdf, ps.