{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T05:40:15Z","timestamp":1695879615376},"reference-count":3,"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":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The ambiguous type theory ATT is introduced in [1] in order to obtain a new proof of Specker's theorem on typical ambiguity [3]. In the present paper we imbed the recursively undecidable theory TR of a single transitive\u2010reflexive relation in an arbitrary stratified theory T such that T \u2ac5 ATT and so reduce the problem of derivability in TR to the same problem for T. From this it follows that ATT is hereditarily undecidable, i.e. ATT has no decidable subtheories.<\/jats:p>","DOI":"10.1002\/malq.19920380126","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:44:06Z","timestamp":1180417446000},"page":"299-300","source":"Crossref","is-referenced-by-count":0,"title":["THE AMBIGUOUS TYPE THEORY IS HEREDITARILY UNDECIDABLE"],"prefix":"10.1002","volume":"38","author":[{"given":"Andrey A.","family":"Kuzichev","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","first-page":"495","article-title":"A theory of ambiguous types and its axiomatizations","volume":"35","author":"Kuzichev A. A.","year":"1989","journal-title":"This Zeitschrift"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/1969974"},{"key":"e_1_2_1_4_2","first-page":"116","volume-title":"Logic, Methodology and Phyilosophy of Science, Proceedings of the International Congress, Stanford, California, 1960","author":"Specker E.","year":"1962"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380126","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380126","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:33:57Z","timestamp":1695846837000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380126"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380126","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}