Degree Year

2010

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Advisor(s)

Elizabeth Wilmer

Committee Member(s)

Michael Henle
Steve Abbott

Keywords

Large cardinal, Set theory, Measurable cardinal, Inaccessible cardinal

Abstract

Infinite sets are a fundamental object of modern mathematics. Surprisingly, the existence of infinite sets cannot be proven within mathematics. Their existence, or even the consistency of their possible existence, must be justified extra-mathematically or taken as an article of faith. We describe here several varieties of large infinite set that have a similar status in mathematics to that of infinite sets, i.e. their existence cannot be proven, but they seem both reasonable and useful. These large sets are known as large cardinals. We focus on two types of large cardinal: inaccessible cardinals and measurable cardinals. Assuming the existence of a measurable cardinal allows us to disprove a questionable statement known as the Axiom of Constructibility (V=L).

Included in

Mathematics Commons

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