Partition Properties for Non-Ordinal Sets under the Axiom of Determinacy

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In this paper we explore coloring theorems for the reals, its quotients, cardinals, and their combinations. This work is done under the scope of the axiom of determinacy. We also explore generalizations of Mycielski's theorem and show how these can be used to establish coloring theorems. To finish, we discuss the strange realm of long unions.

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Holshouser, Jared Kenneth May 2017.

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  • Holshouser, Jared Kenneth

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In this paper we explore coloring theorems for the reals, its quotients, cardinals, and their combinations. This work is done under the scope of the axiom of determinacy. We also explore generalizations of Mycielski's theorem and show how these can be used to establish coloring theorems. To finish, we discuss the strange realm of long unions.

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  • May 2017

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  • July 12, 2017, 3:17 a.m.

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Holshouser, Jared Kenneth. Partition Properties for Non-Ordinal Sets under the Axiom of Determinacy, dissertation, May 2017; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc984121/: accessed December 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .