Results and Proofs of Independence in Combinatorial Set Theory

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Results and Proofs of Independence in Combinatorial Set Theory

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dc.contributor.advisor Kurepa, Đuro
dc.contributor.author Todorčević, Stevo en_US
dc.date.accessioned 2009-12-03T12:20:38Z
dc.date.available 2009-12-03T12:20:38Z
dc.identifier.uri http://hdl.handle.net/123456789/316
dc.description.abstract The thesis consists of four chapters and one appendix. The relation between trees and ordering types, especially the relation between tree-subtree and the type-subtype are considered in Chapter 1. By using Jensens’s principle, Aronszajn’s tree which does not contain any Aronszajn’s subtree and Cantor’s subtree are constructed. Moreover, it is shown that in the model ZFC+GCH each ω_2- Aronszajn’s tree contains Aronszajn’s and Cantor’s subtree. In the first part of Chapter 2 the problem of the existence of Boolean algebras which have non-trivial automorphisms and endomorptisms are studied. It is shown that for each cardinal k, k>ω, there are exactly 2^k types of isomorphic Boolean algebras without non-trivial automorphisms. In the second part of that chapter the problem of isomorphism and automorhism of ω_1-trees is studied. It is shown that there are 2^ω1 types of isomorphic total rigid Aronszajn’s trees, so one Aronszajn’s tree does not have any nontrivial automorphism. Several problems of the partition relations of cardinal numbers are solved in Chapter 3. The appendix contains the proof of the property that in ZFC the σ-dense partial ordered set of power ω_1 does not exist. It is shown that in ZFC there is not any linearly ordered topological space with weight less or equal ω_1 which satisfies Kurepa’s generalization of the notion of separable topological space. It is also shown that if ¬ω Kurepa’s hypothesis + Martin’s axiom + ¬Continuum hypothesis is assumed, then each perfect normal non - Arhimedian space whose weight is ω1 is measurable. en
dc.description.provenance Made available in DSpace on 2009-12-03T12:20:38Z (GMT). No. of bitstreams: 1 phdStevoTodorcevic.pdf: 18198492 bytes, checksum: 58135d69dd1d9de5a69c0ecadd791f65 (MD5) en
dc.publisher Belgrade en_US
dc.title Results and Proofs of Independence in Combinatorial Set Theory en_US
dc.title.alternative Rezultati i dokazi nezavisnosti u kombinatornoj teoriji skupova sr
mf.subject.keywords combinatorial set theory, Aronszajn’s trees, Cantor’s tree, linearly ordered topological spaces, Continuum hypothesis
mf.contributor.committee Devlin, K.J.; Marjanović, Milisav; Prešić, Slaviša

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