Positive indiscernibles

Abstract: We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str

_{0}

-trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so we prove stronger versions for basing -- rather than locally basing or EM-basing -- str-trees on s-trees and str

_{0}

-trees on str-trees. As an application we show that a thick positive theory has

k

-TP

_{2}

iff it has

2

-TP

_{2}

.

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Subsystems of classical logic (including intuitionistic logic) (03B20) Abstract model theory (03C95)

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