DC FieldValueLanguage
dc.contributor.authorTodorčević, Stevoen
dc.date.accessioned2020-05-01T20:29:30Z-
dc.date.available2020-05-01T20:29:30Z-
dc.date.issued1983-01-01en
dc.identifier.issn0024-6107en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/2275-
dc.description.abstractLet (Ai i e{open) I) be an indexed family of nonempty intervals of a linearly ordered set (L, <). Let (I, E) be the intersection graph of (Ai i e{open) I), that is (i, j)e{open) E if and only if Ai∩ Aj ø. In [6], R. Rado considered the following sentence R(k), where K is a cardinal number. If Chr(J, E ∩ [J]2) ≤ K for all J ⊆ I, J ≤ K+, then Chr(I, E) ≤ k. He proved (see [6, Theorem 2]) that R(k) holds for every finite k, and conjectured (see [6, Conjecture 1]) that R(k) holds for every cardinal K. In this note we show that if R(N0) holds, then there is an inner model of set theory with many measurable cardinals. On the other hand, using consistency of the existence of a supercompact cardinal, we prove that R(N0) is consistent with the usual axioms of set theory. We also prove a few results about the intersection graph of (Ai i e{open) I).en
dc.publisherLondon Mathematical Society-
dc.relation.ispartofJournal of the London Mathematical Societyen
dc.titleOn a conjecture of R. Radoen
dc.typeArticleen
dc.identifier.doi10.1112/jlms/s2-27.1.1en
dc.identifier.scopus2-s2.0-0001771462en
dc.relation.firstpage1en
dc.relation.lastpage8en
dc.relation.issue1en
dc.relation.volumeS2-27en
dc.description.rankM22-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0003-4543-7962-
Show simple item record

SCOPUSTM   
Citations

23
checked on Jun 23, 2024

Page view(s)

38
checked on May 9, 2024

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.