{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T11:19:32Z","timestamp":1772450372535,"version":"3.50.1"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"KIAS Individual Grant","award":["CG079801"],"award-info":[{"award-number":["CG079801"]}]},{"name":"KIAS Individual Grant","award":["6G091801"],"award-info":[{"award-number":["6G091801"]}]},{"name":"National Research Foundation of Korea (NRF) Grants","award":["2021R1A2C1009639"],"award-info":[{"award-number":["2021R1A2C1009639"]}]},{"name":"KIAS Individual Grant","award":["SP089701"],"award-info":[{"award-number":["SP089701"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:p> We prove the preservation theorems for NATP; many of them extend the previously established preservation results for other model-theoretic tree properties. Using them, we also furnish proper examples of NATP theories which are simultaneously TP<jats:sub>2<\/jats:sub> and SOP. <\/jats:p><jats:p> First, we show that NATP is preserved by the parametrization and sum of the theories of Fra\u00efss\u00e9 limits of Fra\u00efss\u00e9 classes satisfying strong amalgamation property. <\/jats:p><jats:p> Second, the preservation of NATP for two kinds of dense\/co-dense expansions, i.e. the theories of lovely pairs and of H-structures for geometric theories, and dense\/co-dense expansion on vector spaces is proved. <\/jats:p><jats:p> Next, we prove the preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also the preservation of NTP<jats:sub>1<\/jats:sub> and NTP<jats:sub>2<\/jats:sub> is considered. <\/jats:p><jats:p> Finally, we present some proper examples of NATP theories using the results proved in this paper, including the parametrization of DLO and the expansion of an algebraically closed field by adding a generic linear order. In particular, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP. <\/jats:p>","DOI":"10.1142\/s0219061324500120","type":"journal-article","created":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T11:08:36Z","timestamp":1699873716000},"source":"Crossref","is-referenced-by-count":1,"title":["Preservation of NATP"],"prefix":"10.1142","volume":"25","author":[{"given":"Jinhoo","family":"Ahn","sequence":"first","affiliation":[{"name":"School of Computational Sciences, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, South Korea"}]},{"given":"Joonhee","family":"Kim","sequence":"additional","affiliation":[{"name":"School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, South Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4745-8663","authenticated-orcid":false,"given":"Hyoyoon","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, South Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2150-6145","authenticated-orcid":false,"given":"Junguk","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Changwon National University, 20 Changwondaehak-ro, Uichang-gu, Changwon-si, Gyeongsangnam-do 51140, South Korea"}]}],"member":"219","published-online":{"date-parts":[[2023,12,20]]},"reference":[{"key":"S0219061324500120BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061322500210"},{"key":"S0219061324500120BIB005","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201400056"},{"key":"S0219061324500120BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2009.10.004"},{"key":"S0219061324500120BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00029-015-0190-1"},{"key":"S0219061324500120BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2013.10.002"},{"key":"S0219061324500120BIB009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02498-8"},{"key":"S0219061324500120BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(98)00021-9"},{"key":"S0219061324500120BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-019-1836-z"},{"key":"S0219061324500120BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061316500094"},{"key":"S0219061324500120BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-018-0609-4"},{"key":"S0219061324500120BIB015","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201600049"},{"key":"S0219061324500120BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2003.11.001"},{"key":"S0219061324500120BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-012-0087-z"},{"key":"S0219061324500120BIB018","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1984-0742419-0"},{"key":"S0219061324500120BIB019","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574"},{"key":"S0219061324500120BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.02.001"},{"key":"S0219061324500120BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-013-0363-6"},{"key":"S0219061324500120BIB022","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061321500100"},{"key":"S0219061324500120BIB025","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1333566647"},{"key":"S0219061324500120BIB026","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107415133"},{"key":"S0219061324500120BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.05.012"},{"key":"S0219061324500120BIB028","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139015417"},{"key":"S0219061324500120BIB031","doi-asserted-by":"publisher","DOI":"10.1002\/1521-3870(200101)47:1<45::AID-MALQ45>3.0.CO;2-A"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061324500120","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T02:37:04Z","timestamp":1744252624000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061324500120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,20]]},"references-count":23,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["10.1142\/S0219061324500120"],"URL":"https:\/\/doi.org\/10.1142\/s0219061324500120","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,20]]},"article-number":"2450012"}}