{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:55Z","timestamp":1753889935888,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,9,26]],"date-time":"2017-09-26T00:00:00Z","timestamp":1506384000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,9,26]],"date-time":"2017-09-26T00:00:00Z","timestamp":1506384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,9,26]],"date-time":"2017-09-26T00:00:00Z","timestamp":1506384000000},"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>We consider a special case of Dickson's lemma: for any two functions $f,g$ on the natural numbers there are two numbers $i&amp;lt;j$ such that both $f$ and $g$ weakly increase on them, i.e., $f_i\\le f_j$ and $g_i \\le g_j$. By a combinatorial argument (due to the first author) a simple bound for such $i,j$ is constructed. The combinatorics is based on the finite pigeon hole principle and results in a descent lemma. From the descent lemma one can prove Dickson's lemma, then guess what the bound might be, and verify it by an appropriate proof. We also extract (via realizability) a bound from (a formalization of) our proof of the descent lemma.   Keywords: Dickson's lemma, finite pigeon hole principle, program extraction from proofs, non-computational quantifiers.<\/jats:p>","DOI":"10.23638\/lmcs-13(3:30)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:34:22Z","timestamp":1743701662000},"source":"Crossref","is-referenced-by-count":0,"title":["A bound for Dickson's lemma"],"prefix":"10.23638","volume":"Volume 13, Issue 3","author":[{"given":"Josef","family":"Berger","sequence":"first","affiliation":[]},{"given":"Helmut","family":"Schwichtenberg","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,9,26]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1503.03325v2","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1503.03325v2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:34:22Z","timestamp":1743701662000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3954"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,26]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(3:30)2017","relation":{"is-same-as":[{"id-type":"arxiv","id":"1503.03325","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1503.03325","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,9,26]]},"article-number":"3954"}}