Non-standard lattices and o-minimal groups (Q2837762)
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scientific article; zbMATH DE number 6186898
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-standard lattices and o-minimal groups |
scientific article; zbMATH DE number 6186898 |
Statements
Non-standard lattices and o-minimal groups (English)
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11 July 2013
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o-minimality
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non-standard lattices
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\(\vee\)-definable groups
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dimension
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semi-bounded structures
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generic elements.
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The author studies definable groups in the o-minimal setting by considering three cases of an o-minimal expansion of an ordered group: the field case, the semi-bounded case and the linear case. The notion of a lattice of rank \(m\) in an arbitrary first-order structure is introduced. Both this notion and also \(\vee\)-definable groups are used to describe some structure theorems for o-minimal groups in a broader uniform context. He also studies the group behaviour locally, around suitable generic elements.
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