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oberlin1279129907.pdf (220.53 KB)
ETD Abstract Container
Abstract Header
Large Cardinals
Author Info
Pechenik, Oliver
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1279129907
Abstract Details
Year and Degree
2010, BA, Oberlin College, Mathematics.
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
).
Committee
Elizabeth Wilmer (Advisor)
Michael Henle (Committee Member)
Steve Abbott (Committee Member)
Pages
20 p.
Subject Headings
Mathematics
Keywords
large cardinal
;
set theory
;
measurable cardinal
;
inaccessible cardinal
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Citations
Pechenik, O. (2010).
Large Cardinals
[Undergraduate thesis, Oberlin College]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1279129907
APA Style (7th edition)
Pechenik, Oliver.
Large Cardinals.
2010. Oberlin College, Undergraduate thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1279129907.
MLA Style (8th edition)
Pechenik, Oliver. "Large Cardinals." Undergraduate thesis, Oberlin College, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1279129907
Chicago Manual of Style (17th edition)
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Document number:
oberlin1279129907
Download Count:
2,254
Copyright Info
© 2010, all rights reserved.
This open access ETD is published by Oberlin College Honors Theses and OhioLINK.