{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T17:31:25Z","timestamp":1747157485861,"version":"3.40.4"},"reference-count":6,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T00:00:00Z","timestamp":1728864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T00:00:00Z","timestamp":1728864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["21K03336"],"award-info":[{"award-number":["21K03336"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100019084","name":"Kobe University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100019084","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We investigate the class of <jats:italic>m<\/jats:italic>-hypergraphs whose substructures with <jats:italic>l<\/jats:italic> elements have more than <jats:italic>s<\/jats:italic>\n            <jats:italic>m<\/jats:italic>-element subsets that do not form a hyperedge. The class will have the free amalgamation property if <jats:italic>s<\/jats:italic> is small, but it does not if <jats:italic>s<\/jats:italic> is large. We find the boundary of <jats:italic>s<\/jats:italic>. Suppose the class has the free amalgamation property. In the case <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$m \\ge 3$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>m<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>, we demonstrate that the random structure for the class has continuum-many automorphisms with a single orbit. The situation differs from the case of Henson graphs. In the case of generic hypergraphs constructed by Hrushovski\u2019s method using a predimension function, we also demonstrate that they have no automorphisms with a single orbit.\n<\/jats:p>","DOI":"10.1007\/s00153-024-00944-3","type":"journal-article","created":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T01:01:36Z","timestamp":1728867696000},"page":"423-433","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Random structures and automorphisms with a single orbit"],"prefix":"10.1007","volume":"64","author":[{"given":"Hirotaka","family":"Kikyo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akito","family":"Tsuboi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,14]]},"reference":[{"key":"944_CR1","doi-asserted-by":"publisher","first-page":"69","DOI":"10.2140\/pjm.1971.38.69","volume":"38","author":"CW Henson","year":"1971","unstructured":"Henson, C.W.: A family of countable homogeneous graphs. Pac. J. Math. 38, 69\u201383 (1971). https:\/\/doi.org\/10.2140\/pjm.1971.38.69","journal-title":"Pac. J. Math."},{"key":"944_CR2","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF02582937","volume":"1","author":"PJ Cameron","year":"1985","unstructured":"Cameron, P.J.: Cyclic automorphisms of a countable graph and random sum-free sets. Graphs Comb. 1, 129\u2013135 (1985). https:\/\/doi.org\/10.1007\/BF02582937","journal-title":"Graphs Comb."},{"key":"944_CR3","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1093\/oso\/9780198534686.003.0006","volume-title":"Automorphisms of First-Order Structures","author":"FO Wagner","year":"1994","unstructured":"Wagner, F.O.: Relational structures and dimensions. In: Kaye, R., Macpherson, D. (eds.) Automorphisms of First-Order Structures, pp. 153\u2013180. Oxford University Press, Oxford (1994)"},{"key":"944_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3002-0","volume-title":"Simple Theories","author":"FO Wagner","year":"2000","unstructured":"Wagner, F.O.: Simple Theories. Kluwer, Dordrecht (2000)"},{"key":"944_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574","volume-title":"Model Theory","author":"W Hodges","year":"1993","unstructured":"Hodges, W.: Model Theory. Cambridge University Press, Cambridge (1993)"},{"issue":"2","key":"944_CR6","doi-asserted-by":"publisher","first-page":"580","DOI":"10.2178\/jsl\/1333566638","volume":"77","author":"J Brody","year":"2012","unstructured":"Brody, J., Laskowski, M.C.: On rational limits of Shelah-Spencer graphs. J. Symb. Log. 77(2), 580\u2013592 (2012). https:\/\/doi.org\/10.2178\/jsl\/1333566638","journal-title":"J. Symb. Log."}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-024-00944-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-024-00944-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-024-00944-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T02:58:15Z","timestamp":1745549895000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-024-00944-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,14]]},"references-count":6,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["944"],"URL":"https:\/\/doi.org\/10.1007\/s00153-024-00944-3","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"type":"print","value":"0933-5846"},{"type":"electronic","value":"1432-0665"}],"subject":[],"published":{"date-parts":[[2024,10,14]]},"assertion":[{"value":"27 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 September 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 October 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}