{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T17:11:37Z","timestamp":1777396297539,"version":"3.51.4"},"reference-count":22,"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":14346,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1974,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For each<jats:italic>n<\/jats:italic>&gt; 0, two alternative axiomatizations of the theory of strings over<jats:italic>n<\/jats:italic>alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the<jats:italic>Wahrheitsbegriff<\/jats:italic>and uses the<jats:italic>n<\/jats:italic>characters and concatenation as primitives. The other class involves using<jats:italic>n<\/jats:italic>character-prefixing operators as primitives and derives from Hermes'<jats:italic>Semiotik<\/jats:italic>. All underlying logics are second order. It is shown that, for each<jats:italic>n<\/jats:italic>, the two theories are synonymous in the sense of deBouvere. It is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are synonymous with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories.<\/jats:p>","DOI":"10.2307\/2272846","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:32:58Z","timestamp":1146951178000},"page":"625-637","source":"Crossref","is-referenced-by-count":52,"title":["String theory"],"prefix":"10.1017","volume":"39","author":[{"given":"John","family":"Corcoran","sequence":"first","affiliation":[]},{"given":"William","family":"Frank","sequence":"additional","affiliation":[]},{"given":"Michael","family":"Maloney","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200077100_ref013","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"},{"key":"S0022481200077100_ref022","volume-title":"Logic, semantics and metamathematics","author":"Tarski","year":"1934"},{"key":"S0022481200077100_ref015","volume-title":"Truth and denotation","author":"Martin","year":"1958"},{"key":"S0022481200077100_ref003","volume-title":"Introduction to mathematical logic","author":"Church","year":"1944"},{"key":"S0022481200077100_ref014","unstructured":"Maloney Michael J. , Logical and axiomatic foundations for the study of formal languages and symbolic computation, unpublished Ph.D. dissertation, University of Pennsylvania, 1969. Available from University Microfilms, Ann Arbor, Michigan."},{"key":"S0022481200077100_ref007","article-title":"Logical synonymity","volume":"27","author":"deBouvere","year":"1965","journal-title":"Indagationes Mathematica"},{"key":"S0022481200077100_ref008","volume-title":"The theory of models (Proceedings of the 1963 International Symposium at Berkeley)","author":"deBouvere","year":"1965"},{"key":"S0022481200077100_ref010","first-page":"201\u2013208","volume":"18","author":"Henkin","year":"1953","journal-title":"Banishing the rule of substitution for functional variables"},{"key":"S0022481200077100_ref009","volume-title":"Essays on the theory of numbers","author":"Dedekind","year":"1963"},{"key":"S0022481200077100_ref018","doi-asserted-by":"crossref","DOI":"10.4159\/9780674042469","volume-title":"Mathematical logic","author":"Quine","year":"1951"},{"key":"S0022481200077100_ref002","doi-asserted-by":"crossref","DOI":"10.1515\/9783112316009","volume-title":"Syntactic structures","author":"Chomsky","year":"1957"},{"key":"S0022481200077100_ref021","volume-title":"Logic, semantics and metamathematics","author":"Tarski","year":"1931"},{"key":"S0022481200077100_ref006","doi-asserted-by":"publisher","DOI":"10.2307\/2106718"},{"key":"S0022481200077100_ref019","volume-title":"Mathematical logic","author":"Robbin","year":"1969"},{"key":"S0022481200077100_ref011","volume-title":"Forschungen zur Logik und zur Grundlage der exakten Wissenschaften","author":"Hermes","year":"1938"},{"key":"S0022481200077100_ref017","volume":"11","author":"Quine","year":"1946","journal-title":"Concatenation as a basis for arithmetic"},{"key":"S0022481200077100_ref012","volume-title":"From Frege to G\u00f6del","author":"Hilbert","year":"1927"},{"key":"S0022481200077100_ref004","volume-title":"Introduction to mathematical logic","author":"Church","year":"1956"},{"key":"S0022481200077100_ref005","first-page":"366\u2013367","volume":"36","author":"Corcoran","year":"1971","journal-title":"A semantic definition of definition"},{"key":"S0022481200077100_ref016","volume-title":"Formal systems and recursive functions","author":"Montague","year":"1965"},{"key":"S0022481200077100_ref001","volume-title":"Logical syntax of language","author":"Carnap","year":"1934"},{"key":"S0022481200077100_ref020","volume-title":"Undecidable theories","author":"Tarski","year":"1953"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200077100","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T20:18:19Z","timestamp":1627330699000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200077100\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,12]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1974,12]]}},"alternative-id":["S0022481200077100"],"URL":"https:\/\/doi.org\/10.2307\/2272846","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1974,12]]}}}