{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:42:05Z","timestamp":1753890125175,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T00:00:00Z","timestamp":1512000000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T00:00:00Z","timestamp":1512000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T00:00:00Z","timestamp":1512000000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>The technique known as Grilliot's trick constitutes a template for explicitly defining the Turing jump functional $(\\exists^2)$ in terms of a given effectively discontinuous type two functional. In this paper, we discuss the standard extensionality trick: a technique similar to Grilliot's trick in Nonstandard Analysis. This nonstandard trick proceeds by deriving from the existence of certain nonstandard discontinuous functionals, the Transfer principle from Nonstandard analysis limited to $\\Pi_1^0$-formulas; from this (generally ineffective) implication, we obtain an effective implication expressing the Turing jump functional in terms of a discontinuous functional (and no longer involving Nonstandard Analysis). The advantage of our nonstandard approach is that one obtains effective content without paying attention to effective content. We also discuss a new class of functionals which all seem to fall outside the established categories. These functionals directly derive from the Standard Part axiom of Nonstandard Analysis.<\/jats:p><jats:p>Comment: 21 pages<\/jats:p>","DOI":"10.23638\/lmcs-13(4:23)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:35:34Z","timestamp":1743701734000},"source":"Crossref","is-referenced-by-count":1,"title":["Grilliot's trick in Nonstandard Analysis"],"prefix":"10.23638","volume":"Volume 13, Issue 4","author":[{"given":"Sam","family":"Sanders","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,11,30]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1706.06663v2","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1706.06663v2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:35:35Z","timestamp":1743701735000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,30]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(4:23)2017","relation":{"is-same-as":[{"id-type":"arxiv","id":"1706.06663","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1706.06663","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,11,30]]},"article-number":"4114"}}