{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T07:49:35Z","timestamp":1775461775621,"version":"3.50.1"},"reference-count":13,"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":12703,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,6]]},"abstract":"<jats:p>In recent years there has been a proliferation of logics which extend first-order logic, e.g., logics with infinite sentences, logics with cardinal quantifiers such as \u201cthere exist infinitely many\u2026\u201d and \u201cthere exist uncountably many\u2026\u201d, and a weak second-order logic with variables and quantifiers for finite sets of individuals. It is well known that first-order logic has a limited ability to express many of the concepts studied by mathematicians, e.g., the concept of a wellordering. However, first-order logic, being among the simplest logics with applications to mathematics, does have an extensively developed and well understood model theory. On the other hand, full second-order logic has all the expressive power needed to do mathematics, but has an unworkable model theory. Indeed, the search for a logic with a semantics complex enough to say something, yet at the same time simple enough to say something<jats:italic>about<\/jats:italic>, accounts for the proliferation of logics mentioned above. In this paper, a number of proposed strengthenings of first-order logic are examined with respect to their relative expressive power, i.e., given two logics, what concepts can be expressed in one but not the other?<\/jats:p><jats:p>For the most part, the notation is standard. Most of the notation is either explained in the text or can be found in the book [2] of Chang and Keisler. Some notational conventions used throughout the text are listed below: the empty set is denoted by \u2205.<\/jats:p>","DOI":"10.2307\/2273723","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:50:09Z","timestamp":1146952209000},"page":"129-146","source":"Crossref","is-referenced-by-count":9,"title":["The relative expressive power of some logics extending first-order logic"],"prefix":"10.1017","volume":"44","author":[{"given":"John","family":"Cowles","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048878_ref013","volume-title":"Modern algebra. I","author":"van der Waerden","year":"1964"},{"key":"S0022481200048878_ref008","doi-asserted-by":"crossref","first-page":"97","DOI":"10.4064\/fm-29-1-97-100","article-title":"Les types d'ordre d\u00e9finissables et les ensembles boreliens","volume":"28","author":"Kuratowski","year":"1937","journal-title":"Fundamenta Mahematicae"},{"key":"S0022481200048878_ref003","volume-title":"Decision procedures for real and p-adic fields","author":"Cohen","year":"1967"},{"key":"S0022481200048878_ref005","volume-title":"Lectures in abstract algebra, vol. III, Theory of fields and Galois theory","author":"Jacobson","year":"1964"},{"key":"S0022481200048878_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90019-5"},{"key":"S0022481200048878_ref001","volume-title":"Models and ultraproducts: An introduction","author":"Bell","year":"1969"},{"key":"S0022481200048878_ref007","volume-title":"Elements of mathematical logic, Model theory","author":"Kreisel","year":"1971"},{"key":"S0022481200048878_ref002","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200048878_ref006","first-page":"117","article-title":"On completeness in cardinality logics","volume":"23","author":"Jensen","year":"1975","journal-title":"Bulletin de l'Acad\u00e9mie Pol\u00f2\u01f9aise des Sciences. S\u00e9rie des Sciences Math\u00e9matiques, Astronomiques et Physiques"},{"key":"S0022481200048878_ref011","unstructured":"Nadel M. and Stavi J. , L\u221e\u03bb-equivalence, isomorphism and potential isomorphism (to appear)."},{"key":"S0022481200048878_ref004","unstructured":"Cowles J. R. , Abstract logic and extensions of first order logic, Ph.D. Thesis, The Pennsylvania State University, University Park, 1975"},{"key":"S0022481200048878_ref009","volume-title":"Set theory","author":"Kuratowski","year":"1968"},{"key":"S0022481200048878_ref012","volume-title":"Saturated model theory","author":"Sacks","year":"1972"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048878","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T20:19:42Z","timestamp":1627330782000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048878\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,6]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1979,6]]}},"alternative-id":["S0022481200048878"],"URL":"https:\/\/doi.org\/10.2307\/2273723","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,6]]}}}