{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:15:25Z","timestamp":1753884925128,"version":"3.41.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"NSF","award":["DMS-1600228"],"award-info":[{"award-number":["DMS-1600228"]}]},{"name":"NSF","award":["DMS-1606455"],"award-info":[{"award-number":["DMS-1606455"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:p>We say that a theory [Formula: see text] satisfies arithmetic-is-recursive if any [Formula: see text]-computable model of [Formula: see text] has an [Formula: see text]-computable copy; that is, the models of [Formula: see text] satisfy a sort of jump inversion. We give an example of a theory satisfying arithmetic-is-recursive non-trivially and prove that the theories satisfying arithmetic-is-recursive on a cone are exactly those theories with countably many [Formula: see text]-back-and-forth types.<\/jats:p>","DOI":"10.1142\/s0219061321500215","type":"journal-article","created":{"date-parts":[[2020,11,21]],"date-time":"2020-11-21T17:16:54Z","timestamp":1605979014000},"source":"Crossref","is-referenced-by-count":1,"title":["The property \u201carithmetic-is-recursive\u201d on a cone"],"prefix":"10.1142","volume":"21","author":[{"given":"Uri","family":"Andrews","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew","family":"Harrison-Trainor","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand 6012, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noah","family":"Schweber","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,4,17]]},"reference":[{"key":"S0219061321500215BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0860377-7"},{"key":"S0219061321500215BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(86)90048-5"},{"key":"S0219061321500215BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90065-A"},{"key":"S0219061321500215BIB004","series-title":"Studies in Logic and the Foundations of Mathematics","volume-title":"Computable Structures and the Hyperarithmetical Hierarchy","volume":"144","author":"Ash C. 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