Tree indiscernibilities, revisited

Abstract

We give definitions that distinguish between two notions of indiscernibility for a set $\{a_η\mid η\in \W\}$ that saw original use in \cite{sh90}, which we name \textit{$\s$-} and \textit{$\n$-indiscernibility}. Using these definitions and detailed proofs, we prove $\s$- and $\n$-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent to TP${}_1$ or TP${}_2$ that has not seen explication in the literature. In the Appendix, we exposit the proofs of \citep[{App. 2.6, 2.7}]{sh90}, expanding on the details.

submitted

References in corpus (1)

• Ramsey transfer to semi-retractions

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• Henkin constructions of models with size continuum
• Some Remarks on Kim-dividing in NATP Theories
• Preservation of NATP
• Bounded ultraimaginary independence and its total Morley sequences
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