{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T12:45:13Z","timestamp":1748954713128},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,11,18]],"date-time":"2014-11-18T00:00:00Z","timestamp":1416268800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The collapse models of arithmetic are inconsistent, nontrivial models obtained from \u2115 and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A<jats:sub>3<\/jats:sub>, first given by Avron (Avron, 1991), and give a first order axiom system for the finite collapse models. I present some standard arithmetical axioms in addition to a cyclic axiom and prove that these axioms are sound and complete for the cyclic models, reporting a similar result for the heap models. The state of the situation for the each of the kinds of infinite collapse model is, however, left an open question.<\/jats:p>","DOI":"10.1017\/s1755020314000355","type":"journal-article","created":{"date-parts":[[2014,11,18]],"date-time":"2014-11-18T05:14:46Z","timestamp":1416287686000},"page":"529-539","source":"Crossref","is-referenced-by-count":11,"title":["AXIOMS FOR FINITE COLLAPSE MODELS OF ARITHMETIC"],"prefix":"10.1017","volume":"8","author":[{"given":"ANDREW","family":"TEDDER","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,11,18]]},"reference":[{"key":"S1755020314000355_ref14","volume-title":"Exploring Meinong\u2019s Jungle and Beyond","author":"Routley","year":"1980"},{"key":"S1755020314000355_ref13","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093634406"},{"key":"S1755020314000355_ref9","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1208358750"},{"key":"S1755020314000355_ref2","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-1731353"},{"key":"S1755020314000355_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/2695062"},{"key":"S1755020314000355_ref11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004251506208"},{"key":"S1755020314000355_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370439"},{"key":"S1755020314000355_ref5","doi-asserted-by":"publisher","DOI":"10.2307\/2275433"},{"key":"S1755020314000355_ref6","first-page":"133","article-title":"Relevant arithmetic","volume":"5","author":"Meyer","year":"1976","journal-title":"Bulletin of the Section of Logic, Polish Academy of Sciences"},{"key":"S1755020314000355_ref7","doi-asserted-by":"publisher","DOI":"10.2307\/2274145"},{"key":"S1755020314000355_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00258428"},{"key":"S1755020314000355_ref1","doi-asserted-by":"publisher","DOI":"10.2307\/2274919"},{"key":"S1755020314000355_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-006-9031-1"},{"key":"S1755020314000355_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/9781444315028"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020314000355","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,20]],"date-time":"2019-04-20T15:57:59Z","timestamp":1555775879000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020314000355\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,18]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,9]]}},"alternative-id":["S1755020314000355"],"URL":"https:\/\/doi.org\/10.1017\/s1755020314000355","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,18]]}}}