An AEC satisfying the disjoint amalgamation property, has arbitrarily large models
We study AECs without assuming the amalgamation property in general. We do assume the disjoint amalgamation property in a specific cardinality lambda and assume that there is no maximal model in \lambda. Under these hypotheses, we prove the following: 1. for every model, M, of cardinality \lambda, a...
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| Format | Journal Article |
| Language | English |
| Published |
12.04.2014
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| Subjects | |
| Online Access | Get full text |
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| Summary: | We study AECs without assuming the amalgamation property in general. We do
assume the disjoint amalgamation property in a specific cardinality lambda and
assume that there is no maximal model in \lambda.
Under these hypotheses, we prove the following: 1. for every model, M, of
cardinality \lambda, and every \mu>\lambda, we can find a model M^* of
cardinality \mu, extending M. 2.(\lambda,\lambda,\mu)-amalgalmation property:
for every three models M,N,M^* of cardinalities \lambda,\lambda,\mu,
respectively, if M<M^* and M<N then we can amalgamate M^* and N over M. |
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| DOI: | 10.48550/arxiv.1404.3335 |