{"id":{"repo_id":"unt","oai_identifier":"info:ark/67531/metadc2789"},"canonical_url":"https://search.dev.ndltd.org/etd/unt/info:ark/67531/metadc2789","repository":{"repo_id":"unt","name":"University of North Texas","base_url":"https://digital.library.unt.edu/oai/"},"display":{"title":"A Collapsing Result Using the Axiom of Determinancy and the Theory of Possible Cofinalities","abstract":"Assuming the axiom of determinacy, we give a new proof of the strong partition relation on ω1. Further, we present a streamlined proof that J<λ+(a) (the ideal of sets which force cof Π α < λ) is generated from J<λ+(a) by adding a singleton. Combining these results with a polarized partition relation on ω1","abstract_html":"Assuming the axiom of determinacy, we give a new proof of the strong partition relation on ω1. Further, we present a streamlined proof that J&lt;λ+(a) (the ideal of sets which force cof Π α &lt; λ) is generated from J&lt;λ+(a) by adding a singleton. 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