{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T03:32:57Z","timestamp":1648524777004},"reference-count":3,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8685,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:p>The algebraic systems of combinatory spaces [3] and operative spaces [1] have been designed to provide appropriate settings for the development of abstract recursion theory. As shown in [1, Chapter 27], these systems are closely related; namely, every combinatory space has a companion operative space with a storing operation <jats:italic>St<\/jats:italic> such that Skordev recursiveness in the former equals <jats:italic>st<\/jats:italic>-recursiveness in the latter. The problem of characterization of those operative spaces which have companion combinatory spaces was solved in [2] by introducing a class of operative spaces called Skordev spaces and showing that these give an alternative axiomatics of Skordev's combinatory spaces.<\/jats:p><jats:p>In this paper we study operative spaces with two special constants <jats:italic>S<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>S<\/jats:italic><jats:sub>2<\/jats:sub> which, in computer science terms, axiomatize the availability of stacking facility. We establish that any such space has a Skordev subspace and, moreover, all Skordev spaces can be obtained in this way. The construction ensures that <jats:italic>st<\/jats:italic>-recursiveness in the Skordev space concerned is equivalent to recursiveness in <jats:italic>S<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>S<\/jats:italic><jats:sub>2<\/jats:sub> in the wider operative space. Therefore, it quite unexpectedly turns out that Skordev recursiveness can be expressed via relative recursiveness in operative spaces in a straightforward manner, without employing higher spaces as done in [1].<\/jats:p>","DOI":"10.2307\/2274646","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"561-572","source":"Crossref","is-referenced-by-count":0,"title":["Operative vs. combinatory spaces"],"prefix":"10.1017","volume":"55","author":[{"given":"Lyubomir","family":"Ivanov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025962_ref003","volume-title":"Combinatory spaces and recursiveness in them","author":"Skordev","year":"1980"},{"key":"S0022481200025962_ref001","volume-title":"Algebraic recursion theory","author":"Ivanov","year":"1986"},{"key":"S0022481200025962_ref002","article-title":"Skordev spaces","volume":"80","author":"Ivanov","year":"1986","journal-title":"Annuaire de l'Universit\u00e9 de Sofia, Facult\u00e9 de Math\u00e9matiques et M\u00e9canique"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025962","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:13:39Z","timestamp":1558214019000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025962\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200025962"],"URL":"https:\/\/doi.org\/10.2307\/2274646","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}