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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
1996
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/9602216 |
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| _version_ | 1866916145306533888 |
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| author | Kolman, Oren Shelah, Saharon |
| author_facet | Kolman, Oren Shelah, Saharon |
| contents | In the original version of this paper, we assume a theory $T$ that the logic $\mathbb L_{κ, \aleph_{0}}$ is categorical in a cardinal $λ> κ$, and $κ$ is a measurable cardinal. There we prove that the class of model of $T$ of cardinality $<λ$ (but $\geq |T|+κ$) has the amalgamation property; this is a step toward understanding the character of such classes of models.
In this revised version we replaced the class of models of $T$ by $\mathfrak k$, an AEC (abstract elementary class) which has LS-number ${<} \, κ,$ or at least which behave nicely for ultrapowers by $D$, a normal ultra-filter on $κ$.
Presently sub-section \S1A deals with $T \subseteq \mathbb L_{κ^{+}, \aleph_{0}}$ (and so does a large part of the introduction and little in the rest of \S1), but otherwise, all is done in the context of AEC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9602216 |
| institution | arXiv |
| publishDate | 1996 |
| record_format | arxiv |
| spellingShingle | Categoricity and amalgamation for AEC and $ κ$ measurable Kolman, Oren Shelah, Saharon Logic Primary 03C48. Secondary: 03C45, 03C55, 03C75, 03E05, 03E55 In the original version of this paper, we assume a theory $T$ that the logic $\mathbb L_{κ, \aleph_{0}}$ is categorical in a cardinal $λ> κ$, and $κ$ is a measurable cardinal. There we prove that the class of model of $T$ of cardinality $<λ$ (but $\geq |T|+κ$) has the amalgamation property; this is a step toward understanding the character of such classes of models. In this revised version we replaced the class of models of $T$ by $\mathfrak k$, an AEC (abstract elementary class) which has LS-number ${<} \, κ,$ or at least which behave nicely for ultrapowers by $D$, a normal ultra-filter on $κ$. Presently sub-section \S1A deals with $T \subseteq \mathbb L_{κ^{+}, \aleph_{0}}$ (and so does a large part of the introduction and little in the rest of \S1), but otherwise, all is done in the context of AEC. |
| title | Categoricity and amalgamation for AEC and $ κ$ measurable |
| topic | Logic Primary 03C48. Secondary: 03C45, 03C55, 03C75, 03E05, 03E55 |
| url | https://arxiv.org/abs/math/9602216 |