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Logic"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We study <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\omega $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c9<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-categorical <jats:italic>MS<\/jats:italic>-measurable structures. Our main result is that a certain class of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\omega $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c9<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-categorical Hrushovski constructions, supersimple of finite <jats:italic>SU<\/jats:italic>-rank is not <jats:italic>MS<\/jats:italic>-measurable. These results complement the work of Evans on a conjecture of Macpherson and Elwes. In constrast to Evans\u2019 work, our structures may satisfy independent <jats:italic>n<\/jats:italic>-amalgamation for all <jats:italic>n<\/jats:italic>. We also prove some general results in the context of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\omega $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c9<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-categorical <jats:italic>MS<\/jats:italic>-measurable structures. Firstly, in these structures, the dimension in the <jats:italic>MS<\/jats:italic>-dimension-measure can be chosen to be <jats:italic>SU<\/jats:italic>-rank. Secondly, non-forking independence implies a form of probabilistic independence in the measure. The latter follows from more general unpublished results of Hrushovski, but we provide a self-contained proof.<\/jats:p>","DOI":"10.1007\/s00153-024-00943-4","type":"journal-article","created":{"date-parts":[[2024,10,9]],"date-time":"2024-10-09T16:01:51Z","timestamp":1728489711000},"page":"351-386","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the non-measurability of $$\\omega $$-categorical Hrushovski constructions"],"prefix":"10.1007","volume":"64","author":[{"given":"Paolo","family":"Marimon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,9]]},"reference":[{"key":"943_CR1","unstructured":"Elwes, R.: Dimension and measure in finite first order structures. PhD thesis, School of Mathematics, University of Leeds. https:\/\/citeseerx.ist.psu.edu\/document?repid=rep1&type=pdf &doi=685f35ba345b805b6312edf5779ff7f206a3b5bf. Last accessed: 19th March 2024 (2005)"},{"key":"943_CR2","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1017\/CBO9780511735219.004","volume-title":"Model Theory with Applications to Algebra and Analysis, London Mathematical Society Lecture Note Series; 350","author":"R Elwes","year":"2008","unstructured":"Elwes, R., Macpherson, D.: A survey of asymptotic classes and measurable structures. In: Chatzidakis, Z., Macpherson, D., Pillay, A., et al. (eds.) Model Theory with Applications to Algebra and Analysis, London Mathematical Society Lecture Note Series; 350, vol. 2, pp. 125\u2013160. 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