نمایش مختصر رکورد

dc.contributor.authorKarimi, A.en_US
dc.contributor.authorSalehi, S.en_US
dc.date.accessioned1399-07-09T12:04:08Zfa_IR
dc.date.accessioned2020-09-30T12:04:08Z
dc.date.available1399-07-09T12:04:08Zfa_IR
dc.date.available2020-09-30T12:04:08Z
dc.date.issued2017-10-01en_US
dc.date.issued1396-07-09fa_IR
dc.date.submitted2015-11-01en_US
dc.date.submitted1394-08-10fa_IR
dc.identifier.citationKarimi, A., Salehi, S.. (2017). Diagonal arguments and fixed points. Bulletin of the Iranian Mathematical Society, 43(5), 1073-1088.en_US
dc.identifier.issn1017-060X
dc.identifier.issn1735-8515
dc.identifier.urihttp://bims.iranjournals.ir/article_979.html
dc.identifier.urihttps://iranjournals.nlai.ir/handle/123456789/414692
dc.description.abstract‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fit more theorems in the universal‎ ‎schema of diagonalization‎, ‎such as Euclid's proof for the infinitude of the primes and new proofs of G.~Boolos (1997) for Cantor's theorem on the non-equinumerosity of a set with its powerset‎. ‎Then‎, ‎in Linear Temporal Logic‎, ‎we show the non-existence of a fixed-point in this logic whose proof resembles the argument of Yablo's paradox (1985‎, ‎1993)‎. ‎Thus‎, ‎Yablo's paradox turns for the first time into a genuine mathematico-logical theorem in the framework of Linear Temporal Logic‎. ‎Again the diagonal schema of the paper is used in this proof; and it is also shown that G.~Priest's inclosure schema (1997) can fit in our universal diagonal/fixed-point schema‎. ‎We also show the existence of dominating (Ackermann-like) functions (which dominate a given countable set of functions‎, ‎such as primitive recursive functions) in the schema.en_US
dc.format.extent240
dc.format.mimetypeapplication/pdf
dc.languageEnglish
dc.language.isoen_US
dc.publisherSpringer and the Iranian Mathematical Society (IMS)en_US
dc.relation.ispartofBulletin of the Iranian Mathematical Societyen_US
dc.subjectDiagonal argument‎en_US
dc.subject‎self-reference‎en_US
dc.subject‎fixed-points‎en_US
dc.subject‎Yablo's paradox‎en_US
dc.subject‎(linear) temporal logic‎en_US
dc.subject03-XX Mathematical logic and foundationsen_US
dc.titleDiagonal arguments and fixed pointsen_US
dc.typeTexten_US
dc.typeResearch Paperen_US
dc.contributor.departmentDepartment of Mathematical Sciences‎, ‎Tarbiat Modares University‎, ‎P.O‎. ‎Box 14115--134‎, ‎Tehran‎, ‎Iran.en_US
dc.contributor.departmentResearch Institute for Fundamental Sciences‎, ‎University of Tabriz‎, ‎P.O‎. ‎Box 51666--16471‎, ‎Tabriz‎, ‎Iran‎.en_US
dc.citation.volume43
dc.citation.issue5
dc.citation.spage1073
dc.citation.epage1088


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