On the Consistency of the Failure of Square
<p>Square principles are statements about an important class of infinitary combinatorial objects. They may hold or fail to hold at singular cardinals depending on our large cardinal assumptions, but their precise consistency strengths are not yet known. </p><p> In this paper I pr...
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University of California, Irvine
2013
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ndltd-PROQUEST-oai-pqdtoai.proquest.com-35974312014-01-02T03:57:18Z On the Consistency of the Failure of Square Holben, Ryan Mathematics <p>Square principles are statements about an important class of infinitary combinatorial objects. They may hold or fail to hold at singular cardinals depending on our large cardinal assumptions, but their precise consistency strengths are not yet known. </p><p> In this paper I present two theorems which greatly lower the known upper bounds of the consistency strengths of the failure of several square principles at singular cardinals. I do this using forcing constructions. First, using a quasicompact* cardinal I construct a model of the failure of ¬□([special characters omitted], < ω). Second, using a cardinal which is both subcompact and measurable, I construct a model of □<sub>κ,2</sub> + ¬□<sub> κ</sub> in which κ is singular. This paves the way for several natural extensions of these results.</p> University of California, Irvine 2013-12-28 00:00:00.0 thesis http://pqdtopen.proquest.com/#viewpdf?dispub=3597431 EN |
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NDLTD |
| language |
EN |
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NDLTD |
| topic |
Mathematics |
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Mathematics Holben, Ryan On the Consistency of the Failure of Square |
| description |
<p>Square principles are statements about an important class of infinitary combinatorial objects. They may hold or fail to hold at singular cardinals depending on our large cardinal assumptions, but their precise consistency strengths are not yet known. </p><p> In this paper I present two theorems which greatly lower the known upper bounds of the consistency strengths of the failure of several square principles at singular cardinals. I do this using forcing constructions. First, using a quasicompact* cardinal I construct a model of the failure of ¬□([special characters omitted], < ω). Second, using a cardinal which is both subcompact and measurable, I construct a model of □<sub>κ,2</sub> + ¬□<sub> κ</sub> in which κ is singular. This paves the way for several natural extensions of these results.</p> |
| author |
Holben, Ryan |
| author_facet |
Holben, Ryan |
| author_sort |
Holben, Ryan |
| title |
On the Consistency of the Failure of Square |
| title_short |
On the Consistency of the Failure of Square |
| title_full |
On the Consistency of the Failure of Square |
| title_fullStr |
On the Consistency of the Failure of Square |
| title_full_unstemmed |
On the Consistency of the Failure of Square |
| title_sort |
on the consistency of the failure of square |
| publisher |
University of California, Irvine |
| publishDate |
2013 |
| url |
http://pqdtopen.proquest.com/#viewpdf?dispub=3597431 |
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AT holbenryan ontheconsistencyofthefailureofsquare |
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1716621828364959744 |