{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:27:51Z","timestamp":1772447271638,"version":"3.50.1"},"reference-count":5,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11424,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,12]]},"abstract":"<jats:p>Les arbres sont les ordres partiels qui v\u00e9rifient l'axiome suppl\u00e9mental \u2200<jats:italic>x<\/jats:italic>\u2200<jats:italic>y<\/jats:italic>\u2200<jats:italic>z<\/jats:italic>(<jats:italic>y<\/jats:italic> \u2264<jats:italic>x<\/jats:italic> \u2227<jats:italic>z<\/jats:italic> \u2264 <jats:italic>x<\/jats:italic> \u2192 <jats:italic>y<\/jats:italic> \u2264 <jats:italic>z<\/jats:italic> \u2228 <jats:italic>z<\/jats:italic> \u2264 <jats:italic>y<\/jats:italic>), i.e. l'ensemble des minorants de chaque \u00e9l\u00e9ment est totalement ordonn\u00e9.<\/jats:p><jats:p>Le principal r\u00e9sultat de cet article concerne l'instabilit\u00e9 des arbres: nous prouvons (\u00a72) qu'aucune th\u00e9orie d'arbre n'a la propri\u00e9t\u00e9 d'ind\u00e9pendance, ce qui g\u00e9n\u00e9ralise un theoreme de Poizat [3] sur les ordres totaux. II s'en suit au moyen d'un resultat d'interpr\u00e9tation [4] qu'aucune th\u00e9orie de structure arborescente n'a la propri\u00e9t\u00e9 d'ind\u00e9pendance; en particulier ceci vaut pour les arbres color\u00e9s.<\/jats:p><jats:p>Le \u00a73 est consacr\u00e9 aux arbres stables. II est prouv\u00e9 qu'un arbre est stable ssi il est superstable ssi il est de hauteur born\u00e9e. Sous l'hypoth\u00e8se de stabilit\u00e9, les arbres premiers, minimaux, et strictement minimaux sont caract\u00e9ris\u00e9s en termes d'al-g\u00e9bricit\u00e9.<\/jats:p>","DOI":"10.2307\/2273103","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:01:43Z","timestamp":1146952903000},"page":"841-853","source":"Crossref","is-referenced-by-count":8,"title":["Th\u00e9ories d'arbres"],"prefix":"10.1017","volume":"47","author":[{"given":"Michel","family":"Parigot","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200043711_ref005","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1978"},{"key":"S0022481200043711_ref004","unstructured":"[4] Schmerl James H. , Arborescent stuctures. II: Interpretability in the theory of trees (preprint)."},{"key":"S0022481200043711_ref003","first-page":"513","volume":"46","author":"Poizat","year":"1981","journal-title":"Th\u00e9ories in stables"},{"key":"S0022481200043711_ref002","unstructured":"[2] Poizat Bruno , D\u00e9viation des types, Th\u00e8se, Universit\u00e9 Pierre et Marie Curie, Paris, 1977."},{"key":"S0022481200043711_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757234"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200043711","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T20:18:19Z","timestamp":1558729099000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200043711\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["S0022481200043711"],"URL":"https:\/\/doi.org\/10.2307\/2273103","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}