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- W2951939365 abstract "We generalize the Unstable Formula Theorem characterization of stable theories from citep{sh78}: 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 citep{sh78}: in our notation, a sequence of parameters from an $L$-structure $M$, $(b_i : i in I)$, indexed by an $L'$-structure $I$ is emph{$L'$-generalized indiscernible in $M$} if qftp$^{L'}(ov{i};I)$=qftp$^{L'}(ov{j};I)$ implies tp$^L(ov{b}_{ov{i}}; M)$ = tp$^L(ov{b}_{ov{j}};M)$ for all same-length, finite $ov{i}, ov{j}$ from $I$. Let $T_g$ be the theory of linearly ordered graphs (symmetric, with no loops) in the language with signature $L_g={<, R}$. Let $K_g$ be the class of all finite models of $T_g$. We show that a theory $T$ has NIP if and only if any $L_g$-generalized indiscernible in a model of $T$ indexed by an $L_g$-structure with age equal to $K_g$ is an indiscernible sequence." @default.
- W2951939365 created "2019-06-27" @default.
- W2951939365 creator A5046955783 @default.
- W2951939365 date "2011-06-25" @default.
- W2951939365 modified "2023-09-27" @default.
- W2951939365 title "Characterization of NIP theories by ordered graph-indiscernibles" @default.
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