Abstract
We give definitions that distinguish between two notions of indiscernibility for a set \({\{a_{\eta} \mid \eta \in ^{\omega>}\omega\}}\) that saw original use in Shelah [Classification theory and the number of non-isomorphic models (revised edition). North-Holland, Amsterdam, 1990], which we name s- and str−indiscernibility. Using these definitions and detailed proofs, we prove s- and str-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent to TP1 or TP2 that has not seen explication in the literature. In the Appendix, we exposit the proofs of Shelah [Classification theory and the number of non-isomorphic models (revised edition). North-Holland, Amsterdam, 1990, App. 2.6, 2.7], expanding on the details.
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The first author was supported by an NRF Grant 2011-0021916. The second author was supported by the second phase of the Brain Korea 21 Program in 2011. The third author was supported by the NSF-AWM Mentoring Travel Grant.
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Kim, B., Kim, HJ. & Scow, L. Tree indiscernibilities, revisited. Arch. Math. Logic 53, 211–232 (2014). https://doi.org/10.1007/s00153-013-0363-6
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DOI: https://doi.org/10.1007/s00153-013-0363-6