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Logic"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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<jats:inline-formula><jats:alternatives><jats:tex-math>$$_0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow\/>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing\u2014rather than locally basing or EM-basing\u2014str-trees on s-trees and str<jats:inline-formula><jats:alternatives><jats:tex-math>$$_0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow\/>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-trees on str-trees. As an application we show that a thick positive theory has <jats:italic>k<\/jats:italic>-<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {TP_2}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>TP<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> iff it has 2-<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {TP_2}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>TP<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><\/jats:p>","DOI":"10.1007\/s00153-024-00928-3","type":"journal-article","created":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T17:01:46Z","timestamp":1715360506000},"page":"921-940","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Positive indiscernibles"],"prefix":"10.1007","volume":"63","author":[{"given":"Mark","family":"Kamsma","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,10]]},"reference":[{"issue":"01","key":"928_CR1","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1142\/S0219061303000212","volume":"03","author":"I Ben-Yaacov","year":"2003","unstructured":"Ben-Yaacov, I.: Positive model theory and compact abstract theories. 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