{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T00:59:09Z","timestamp":1785113949587,"version":"3.55.0"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T00:00:00Z","timestamp":1780444800000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,27]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We present correct and natural development of continuity theory in a predicative set theory called ${\\textsf{PZF}^{\\textsf{U}}}$. This is done by using a delicate and careful choice of those Dedekind cuts that are taken as real numbers. ${\\textsf{PZF}^{\\textsf{U}}}$ is based on ancestral logic rather than on first-order logic. Its key feature is that it is definitional in the sense that every object that is shown in it to exist is defined by some closed term of the theory. This allows for a very concrete, computationally oriented model of it. The development of analysis in ${\\textsf{PZF}^{\\textsf{U}}}$ does not involve coding, and the definitions it provides for the basic notions are the natural ones.<\/jats:p>","DOI":"10.1093\/jigpal\/jzag034","type":"journal-article","created":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T11:13:00Z","timestamp":1776510780000},"source":"Crossref","is-referenced-by-count":0,"title":["Developing continuity theory in a formal predicative set theory"],"prefix":"10.1093","volume":"34","author":[{"given":"Arnon","family":"Avron","sequence":"first","affiliation":[{"name":"School of Computer Science , Tel Aviv University, Tel Aviv, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nissan","family":"Levi","sequence":"additional","affiliation":[{"name":"School of Computer Science , Tel Aviv University, Tel Aviv, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,6,2]]},"reference":[{"key":"2026072620015263700_ref1","volume-title":"Foundations of Databases","author":"Abiteboul","year":"1995"},{"key":"2026072620015263700_ref2","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/978-94-017-0253-9_7","article-title":"Transitive closure and the mechanization of mathematics","volume-title":"Thirty Five Years of Automating Mathematics","author":"Avron A","year":"2003"},{"key":"2026072620015263700_ref3","first-page":"32","article-title":"Formalizing set theory as it is actually used","volume-title":"Proceedings of Mathematical Knowledge Management (MKM 2004), LNCS 3119","author":"Avron","year":"2004"},{"key":"2026072620015263700_ref4","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.tcs.2007.12.008","article-title":"Constructibility and decidability versus domain independence and absoluteness","volume":"394","author":"Avron","year":"2008","journal-title":"Theoret Comp Sci"},{"key":"2026072620015263700_ref5","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/978-3-540-78127-1_6","article-title":"A framework for formalizing set theories based on the use of static set terms","volume-title":"Pillars of Computer Science","author":"Avron","year":"2008"},{"key":"2026072620015263700_ref6","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1515\/9783110324907.31","article-title":"A new approach to predicative set theory","volume-title":"Ways of Proof Theory, volume 2 of Ontos Series in Mathematical Logic","author":"Avron","year":"2010"},{"key":"2026072620015263700_ref7","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1017\/bsl.2020.23","article-title":"Weyl reexamined: das Kontinuum 100 years later","volume":"26","author":"Avron","year":"2020","journal-title":"Bull Symb Log"},{"key":"2026072620015263700_ref8","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1017\/bsl.2024.2","article-title":"Poincar\u00e9-Weyl\u2019s predicativity: going beyond $\\varGamma _0$","volume":"30","author":"Avron A","year":"2024","journal-title":"Bull Symb Log"},{"key":"2026072620015263700_ref9","first-page":"53","article-title":"Formalizing scientifically applicable mathematics in a definitional framework","volume":"9","author":"Avron A","year":"2016","journal-title":"J Formal Reason"},{"key":"2026072620015263700_ref10","doi-asserted-by":"publisher","DOI":"10.23638\/LMCS-14(4:1)2018","article-title":"Applicable mathematics in a minimal computational theory of sets. 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