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  1.  43
    Tree indiscernibilities, revisited.Byunghan Kim, Hyeung-Joon Kim & Lynn Scow - 2014 - Archive for Mathematical Logic 53 (1-2):211-232.
    We give definitions that distinguish between two notions of indiscernibility for a set {aη∣η∈ω>ω}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\{a_{\eta} \mid \eta \in ^{\omega>}\omega\}}$$\end{document} that saw original use in Shelah [Classification theory and the number of non-isomorphic models. 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 (...)
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  2.  21
    Characterization of NIP theories by ordered graph-indiscernibles.Lynn Scow - 2012 - Annals of Pure and Applied Logic 163 (11):1624-1641.
    We generalize the Unstable Formula Theorem characterization of stable theories from Shelah [11], that a theory T is stable just in case any infinite indiscernible sequence in a model of T is an indiscernible set. We use a generalized form of indiscernibles from [11], in our notation, a sequence of parameters from an L-structure M, , indexed by an L′-structure I is L′-generalized indiscernible inM if qftpL′=qftpL′ implies tpL=tpL for all same-length, finite ¯,j from I. Let Tg be the theory (...)
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  3.  29
    Indiscernibles, EM-Types, and Ramsey Classes of Trees.Lynn Scow - 2015 - Notre Dame Journal of Formal Logic 56 (3):429-447.
    The author has previously shown that for a certain class of structures $\mathcal {I}$, $\mathcal {I}$-indexed indiscernible sets have the modeling property just in case the age of $\mathcal {I}$ is a Ramsey class. We expand this known class of structures from ordered structures in a finite relational language to ordered, locally finite structures which isolate quantifier-free types by way of quantifier-free formulas. This result is applied to give new proofs that certain classes of trees are Ramsey. To aid this (...)
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  4.  36
    Ramsey transfer to semi-retractions.Lynn Scow - 2021 - Annals of Pure and Applied Logic 172 (3):102891.
  5.  24
    Characterizing model-theoretic dividing lines via collapse of generalized indiscernibles.Vincent Guingona, Cameron Donnay Hill & Lynn Scow - 2017 - Annals of Pure and Applied Logic 168 (5):1091-1111.
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  6.  25
    Big Ramsey degrees in ultraproducts of finite structures.Dana Bartošová, Mirna Džamonja, Rehana Patel & Lynn Scow - 2024 - Annals of Pure and Applied Logic 175 (7):103439.
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  7.  12
    Products of Classes of Finite Structures.Vince Guingona, Miriam Parnes & Lynn Scow - 2023 - Notre Dame Journal of Formal Logic 64 (4):441-469.
    We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We explore how each of these properties interacts with the lexicographic product, full product, and free superposition of classes of structures. Additionally, we consider the classes of theories which admit configurations indexed by these products. In particular, we show that, under mild assumptions, the products considered in this article do not yield (...)
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  8.  11
    A New Perspective on Semi-Retractions and the Ramsey Property.Dana Bartošová & Lynn Scow - 2024 - Journal of Symbolic Logic 89 (3):945-979.
    We investigate the notion of a semi-retraction between two first-order structures (in typically different signatures) that was introduced by the second author as a link between the Ramsey property and generalized indiscernible sequences. We look at semi-retractions through a new lens establishing transfers of the Ramsey property and finite Ramsey degrees under quite general conditions that are optimal as demonstrated by counterexamples. Finally, we compare semi-retractions to the category theoretic notion of a pre-adjunction.
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