{"id":{"repo_id":"york","oai_identifier":"oai:yorkspace.library.yorku.ca:10315/32107"},"canonical_url":"https://search.dev.ndltd.org/etd/york/oai:yorkspace.library.yorku.ca:10315/32107","repository":{"repo_id":"york","name":"York University","base_url":"https://yorkspace.library.yorku.ca/oai/request"},"display":{"title":"Maximal Saturated Linear Orders","abstract":"The 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.","abstract_html":"The 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.","abstract_has_math":false,"creators":["Kibedi, Francisco Guillermo Justo"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Steprans, Juris"],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-09-20","date_published":"2016-09-20","updated_at":"2026-07-24T06:33:58Z","subjects":["Theoretical mathematics"],"languages":["en"],"rights":["Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10315/32107","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Steprans, Juris"]},{"key":"dc:creator","label":"Author","values":["Kibedi, Francisco Guillermo Justo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-09-20T16:26:52Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-09-20T16:26:52Z"]},{"key":"dc:date.issued","label":"Date","values":["2016-09-20"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Theoretical mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10315/32107"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The 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."]},{"key":"dc:title","label":"Title","values":["Maximal Saturated Linear Orders"]}]}],"canonical_facts":{"dc:contributor.advisor":["Steprans, Juris"],"dc:creator":["Kibedi, Francisco Guillermo Justo"],"dc:date.accessioned":["2016-09-20T16:26:52Z"],"dc:date.available":["2016-09-20T16:26:52Z"],"dc:date.issued":["2016-09-20"],"dc:description.abstract":["The 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.uri":["http://hdl.handle.net/10315/32107"],"dc:language.iso":["en"],"dc:rights":["Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests."],"dc:subject":["Theoretical mathematics"],"dc:title":["Maximal Saturated Linear Orders"],"dc:type":["Electronic Thesis or Dissertation"]},"updated_at":"2026-07-24T06:33:58Z"}