Maximal Saturated Linear Orders

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dc.contributor.advisorSteprans, Juris
dc.creatorKibedi, Francisco Guillermo Justo
dc.date.accessioned2016-09-20T16:26:52Z
dc.date.available2016-09-20T16:26:52Z
dc.date.copyright2015-09-24
dc.date.issued2016-09-20
dc.date.updated2016-09-20T16:26:52Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractThe goal of this dissertation is to prove two theorems related to a question posed by Felix Hausdorff in 1907 regarding pantachies, which are maximal linearly ordered subsets of the space of real-valued sequences partially ordered by eventual domination. Hausdorff's question was as follows: is there a pantachie containing no gaps of order type the first uncountable cardinal? In Chapter 1, some terminology is defined, and Hausdorff's question about pantachies is explored. Some related work by other mathematicians is examined, both preceding and following Hausdorff's paper. In Chapter 2, relevant definitions and results about forcing, gaps, and saturated linear orders are collected. Chapter 3 contains the complete proof of the first theorem, namely, the consistency of the existence of a saturated Hausdorff pantachie in a model where the continuum hypothesis (CH) fails. Finally, in Chapter 4, a different method is used to prove a stronger result, namely, the consistency of the existence of a saturated Hausdorff pantachie in a model of Martin's Axiom along with the negation of CH. The appendix mentions a few related open questions and some partial answers.
dc.identifier.urihttp://hdl.handle.net/10315/32107
dc.language.isoen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectTheoretical mathematics
dc.subject.keywordsSet Theory
dc.subject.keywordsCardinal
dc.subject.keywordsCardinal Arithmetic
dc.subject.keywordsIndependence
dc.subject.keywordsGeneric
dc.subject.keywordsGenericity
dc.subject.keywordsDelta-system
dc.subject.keywordsHausdorff
dc.subject.keywordsFelix Hausdorff
dc.subject.keywordsPantachie
dc.subject.keywordsMaximal linear order
dc.subject.keywordsMaximal
dc.subject.keywordsLinear
dc.subject.keywordsLinear order
dc.subject.keywordsOrder
dc.subject.keywordsPartial order
dc.subject.keywordsSaturated
dc.subject.keywordsSaturated linear order
dc.subject.keywordsMaximal saturated linear order
dc.subject.keywordsSaturation
dc.subject.keywordsEventual domination
dc.subject.keywordsForcing
dc.subject.keywordsForcing Extension
dc.subject.keywordsIterated Forcing
dc.subject.keywordsFinite-support iterated forcing
dc.subject.keywordsGaps
dc.subject.keywordsGap-filling
dc.subject.keywordsPregaps
dc.subject.keywordsCuts
dc.subject.keywordsCut-filling
dc.subject.keywordscontinuum
dc.subject.keywordsContinuum Hypothesis
dc.subject.keywordsMartin’s Axiom
dc.subject.keywordsCH
dc.subject.keywordsMA
dc.subject.keywordsKunen
dc.subject.keywordsPartial Order
dc.subject.keywordsCountable chain condition
dc.subject.keywordsCcc
dc.subject.keywordsSpecial gaps
dc.subject.keywordsStrong gaps
dc.subject.keywordsSuslin Trees
dc.subject.keywordsAronszajn Trees
dc.subject.keywordsPaul du Bois-Reymond
dc.subject.keywordsRates of convergence
dc.subject.keywordsInfinitesimal
dc.subject.keywordsHyper-reals
dc.subject.keywordsUltrapower
dc.subject.keywordsUltrafilter
dc.subject.keywordsIdeal
dc.subject.keywordsDivergence
dc.subject.keywordsDivergence Ordering
dc.subject.keywordsConvergence
dc.subject.keywordsAlmost Containment
dc.subject.keywordsRichard Laver
dc.subject.keywordsInvestigations into Order Types
dc.subject.keywordsUniversal
dc.subject.keywordsUniversal linear order
dc.subject.keywordsBaumgartner
dc.subject.keywordsJames Baumgartner
dc.subject.keywordsKenneth Kunen
dc.subject.keywordsWoodin
dc.subject.keywordsHugh Woodin
dc.subject.keywordsProper Forcing Axiom
dc.subject.keywordsUniform Dense
dc.subject.keywordsSpecial Trees
dc.subject.keywordsSpecializer
dc.subject.keywordsTree-Specializer
dc.subject.keywordsTree-Specializing forcing
dc.subject.keywordsccc-fillable
dc.subject.keywordsccc-indestructible
dc.subject.keywordsPre-caliber
dc.subject.keywordsPre-caliber aleph 1
dc.subject.keywordsModel
dc.subject.keywordsGround model
dc.subject.keywordsCountable transitive model
dc.subject.keywordsZFC
dc.subject.keywordsAntichain
dc.subject.keywordsMaximal antichain
dc.subject.keywordsNice partial order
dc.subject.keywordsKibedi
dc.subject.keywordsFrancisco Kibedi
dc.subject.keywordsSteprans
dc.subject.keywordsJuris Steprans
dc.titleMaximal Saturated Linear Orders
dc.typeElectronic Thesis or Dissertation

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