Abstract
We examine whether certain properties arising from statements equivalent to the Axiom of Choice can be extended to uncountable cardinals. We also examine the relationship between these cardinals and strongly compact cardinals. We end with 3 case scenarios and an open question.
Status
Graduate
Department
Mathematics
College
College of Arts and Sciences
Campus
Athens
Faculty Mentor
Todd Eisworth
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Strongly Compact Cardinals may have surprising properties
We examine whether certain properties arising from statements equivalent to the Axiom of Choice can be extended to uncountable cardinals. We also examine the relationship between these cardinals and strongly compact cardinals. We end with 3 case scenarios and an open question.