{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T05:38:01Z","timestamp":1757309881203,"version":"3.41.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> We show that under the proper forcing axiom the class of all Aronszajn lines behave like [Formula: see text]-scattered orders under the embeddability relation. In particular, we are able to show that the class of better-quasi-order labeled fragmented Aronszajn lines is itself a better-quasi-order. Moreover, we show that every better-quasi-order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees, we are also able to deduce a decomposition result, that for every Aronszajn line [Formula: see text] there is an integer [Formula: see text] such that for any finite coloring of [Formula: see text] there is subset [Formula: see text] of [Formula: see text] isomorphic to [Formula: see text] which uses no more than [Formula: see text] colors. <\/jats:p>","DOI":"10.1142\/s0219061322500179","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T09:18:28Z","timestamp":1655457508000},"source":"Crossref","is-referenced-by-count":1,"title":["Decomposing Aronszajn lines"],"prefix":"10.1142","volume":"23","author":[{"given":"Keegan Dasilva","family":"Barbosa","sequence":"first","affiliation":[{"name":"University of Toronto, 40 St. George Street, Toronto, ON, Canada M5S 2E4, Canada"}]}],"member":"219","published-online":{"date-parts":[[2022,9,27]]},"reference":[{"key":"S0219061322500179BIB001","series-title":"Advanced Courses in Mathematics\u00a0\u2014 CRM Barcelona","doi-asserted-by":"crossref","DOI":"10.1007\/3-7643-7360-1","volume-title":"Ramsey Methods in Analysis","author":"Argyros S. 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