Doctor of Philosophy (PhD)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
Number of Pages
In 1971, Kunen proved that the Axiom of Choice imposes a ceiling on the large cardinal hierarchy . Much like the assumption V ≠ L unlocks measurable cardinals and beyond, dropping the Axiom of Choice enables Reinhardt cardinals and stronger cardinals to be explored. Some major notions of large cardinals beyond choice have recently been standardized by Woodin et. al. , with questions raised regarding their interconnectedness. Part 1 of this dissertation partially answers two of those questions, while conjecturing, with a partial solution, a much stronger answer which would simplify the existing cardinal charts - that Regular Berkeley Cardinals are Club Berkeley Cardinals. Part 2 articulates some variations of the major choiceless cardinals, illuminating an iterating structure between them.
Axiom of Choice; Berkeley Cardinals; Elementary Embeddings; Large Cardinals; Reinhardt Cardinals; Set Theory
University of Nevada, Las Vegas
Linkletter, David, "Exploring the Choiceless Cardinal Hierarchy" (2021). UNLV Theses, Dissertations, Professional Papers, and Capstones. 4168.
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