{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T14:41:39Z","timestamp":1698331299036},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let \u039b denote the semiring of isols. We characterize existential completeness for Nerode subsemirings of \u039b, by means of a purely isol\u2010theoretic \u201c\u03a3<jats:sub>1<\/jats:sub> separation property\u201d. (A \u201cconcrete\u201d characterization that is not \u039b\u2010theoretic is well known: the existentially complete Nerode semirings are the ones that are isomorphic to \u03a3<jats:sub>1<\/jats:sub> ultrapowers.) Our characterization is purely isol\u2010theoretic in that it is formulated entirely in terms of the extensions to \u039b of the \u03a3<jats:sub>1<\/jats:sub> subsets of the natural numbers. Advantage is taken of a special kind of isol first conjectured to exist by Ellentuck and first proven to exist by Barback (unpublished). In addition, we strengthen the negative part of [13] by showing that existential completeness is not secured, for a given Nerode semiring, by either (i) a certain \u201cfunctional closure\u201d property for the extensions of partial recursive functions or (ii) the property of \u201cpulling in\u201d some portion of each partial recursive fiber; these latter results are perhaps a little surprising.<\/jats:p>","DOI":"10.1002\/malq.19950410102","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T23:16:44Z","timestamp":1180826204000},"page":"1-14","source":"Crossref","is-referenced-by-count":1,"title":["Existentially Complete Nerode Semirings"],"prefix":"10.1002","volume":"41","author":[{"given":"Thomas G.","family":"McLaughlin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"Barback J. Isols that are torre and strongly torre for the RE sets. Privately communicated unpublished notes."},{"key":"e_1_2_1_3_2","first-page":"163","article-title":"Tame models in the isols","volume":"12","author":"Barback J.","year":"1986","journal-title":"Houston J. Math."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1090\/S0002-9939-1993-1155592-0","article-title":"On the minimality of tame models in the isols","volume":"119","author":"Barback J.","year":"1993","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19800261302"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757881"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0064082","volume-title":"Forcing, arithmetic, division rings. Lecture Notes in Mathematics","author":"Hirschfeld J.","year":"1975"},{"key":"e_1_2_1_8_2","first-page":"354","article-title":"Enumerable sets are diophantine","volume":"11","author":"Matijasevic Y.","year":"1970","journal-title":"Soviet Math. Doklady"},{"key":"e_1_2_1_9_2","volume-title":"Regressive sets and the theory of isols. Lecture Notes in Pure and Appl. Math","author":"McLaughlin T.","year":"1982"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2046244"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90064-9"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(92)90070-G"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01794985"},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1090\/S0002-9939-1993-1116268-9","article-title":"Recursive fibers of RST isols","volume":"117","author":"McLaughlin T.","year":"1993","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.2307\/1970338"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.2307\/1970455"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410102","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T17:58:03Z","timestamp":1698256683000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410102"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410102"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410102","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}