Abstract Elementary Classes with Lowenheim-Skolem Number Cofinal with Omega
| dc.contributor.advisor | Kueker, David W | en_US |
| dc.contributor.author | Johnson, Gregory Mitchell | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2008-10-11T05:44:31Z | |
| dc.date.available | 2008-10-11T05:44:31Z | |
| dc.date.issued | 2008-08-03 | en_US |
| dc.description.abstract | An abstract elementary class is a class $\aec$ of structures for some vocabulary $L$ together with a ``strong substructure'' relation $\prec_{\aec}$ on $\aec$ satisfying certain axioms. Abstract elementary classes include elementary classes with elementary substructure and classes axiomatizable in $L_{\infty,\omega}$ with elementary substructure relative to some fragment of $L_{\infty,\omega}$. For every abstract elementary class there is some number $\kappa$, called the L\"owenheim-Skolem number, so that every structure in the class has a strong substructure of cardinality $\leq \kappa$. We study abstract elementary classes with L\"owenheim-Skolem number $\kappa$, where $\kappa$ is cofinal with $\omega$, which have finite character. We generalize results obtained by Kueker for $\kappa=\omega$. In particular we show that $\aec$ is closed under $L_{\infty,\kappa}$-elementary equivalence and obtain sufficient conditions for $\aec$ to be $L_{\infty,\kappa}$-axiomatizable. The results depend on developing an appropriate concept of $\kappa$-a.e. | en_US |
| dc.format.extent | 318908 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/8567 | |
| dc.language.iso | en_US | |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | Abstract Elementary Classes | en_US |
| dc.subject.pquncontrolled | Countable Approximations | en_US |
| dc.subject.pquncontrolled | Finite Character | en_US |
| dc.title | Abstract Elementary Classes with Lowenheim-Skolem Number Cofinal with Omega | en_US |
| dc.type | Dissertation | en_US |
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