{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T10:25:56Z","timestamp":1752229556992},"reference-count":2,"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":4699,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1994,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is shown by Parsons [2] that the first\u2010order fragment of Frege's (inconsistent) logical system in the <jats:italic>Grundgesetze der Arithmetic<\/jats:italic> is consistent. In this note we formulate and prove a stronger version of this result for arbitrary first\u2010order theories. We also show that a natural attempt to further strengthen our result runs afoul of Tarski's theorem on the undefinability of truth.<\/jats:p><jats:p><jats:bold>Mathematics Subject Classification:<\/jats:bold> 03B10.<\/jats:p>","DOI":"10.1002\/malq.19940400104","type":"journal-article","created":{"date-parts":[[2007,6,3]],"date-time":"2007-06-03T01:56:29Z","timestamp":1180835789000},"page":"27-30","source":"Crossref","is-referenced-by-count":4,"title":["Fregean Extensions of First\u2010Order Theories"],"prefix":"10.1002","volume":"40","author":[{"given":"John L.","family":"Bell","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","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71252-7"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093636853"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19940400104","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19940400104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T00:49:42Z","timestamp":1698108582000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19940400104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,1]]},"references-count":2,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1994,1]]}},"alternative-id":["10.1002\/malq.19940400104"],"URL":"https:\/\/doi.org\/10.1002\/malq.19940400104","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,1]]}}}