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- W2100446030 abstract "We generalize the Unstable Formula Theorem characterization of stable theories in cite{sh}: 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 cite{sh,shnew}: in our notation, a sequence of parameters from an $L$-structure $M$, $(ov{a}_i : i in I)$, 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$^L(ov{a}_{ov{i}}; M)$ = tp$^L(ov{a}_{ov{j}}; M)$ for all same-length, finite $ov{i}, ov{j}$ from $I$. Let $T_g$ be the theory of linearly ordered symmetric graphs with no loops in the language with signature ${<, R}$, $L_g$. Say that a emph{quantifier-free weakly-saturated} model of an $L$-theory $T$ is some model $M vDash T$ that embeds realizations of all quantifier-free $L$-types consistent with $T$. We show that a theory $T$ is NIP if and only if every quantifier-free weakly-saturated $L_g$-generalized indiscernible in a model of $T$ is an indiscernible sequence. In the process of proving this characterization, a result is introduced relating the utility of generalized indiscernibles indexed by a structure $I$ to the Ramsey-type properties of the structures in age($I$). Results about the previous development of generalized indiscernibles and known results about certain Ramsey-type properties are explicated in the text." @default.
- W2100446030 created "2016-06-24" @default.
- W2100446030 creator A5046955783 @default.
- W2100446030 date "2010-01-01" @default.
- W2100446030 modified "2023-09-27" @default.
- W2100446030 title "Characterization Theorems by Generalized Indiscernibles" @default.
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