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arXiv · 2305.14127

Positive indiscernibles

Mark Kamsma
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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$_2$.

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Mark Kamsma. 2023-05-23. Positive indiscernibles. https://doi.org/10.1007/s00153-024-00928-3

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