Quantifier elimination for o-minimal structures expanded by a valuational cut
Let $R$ be an o-minimal expansion of a group in a language in which $\textrm{Th}(R)$ eliminates quantifiers, and let $C$ be a predicate for a valuational cut in $R$. We identify a condition that implies quantifier elimination for $\textrm{Th}(R,C)$ in the language of $R$ expanded by $C$ and a small...
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| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
15.06.2020
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Let $R$ be an o-minimal expansion of a group in a language in which
$\textrm{Th}(R)$ eliminates quantifiers, and let $C$ be a predicate for a
valuational cut in $R$. We identify a condition that implies quantifier
elimination for $\textrm{Th}(R,C)$ in the language of $R$ expanded by $C$ and a
small number of constants, and which, in turn, is implied by $\textrm{Th}(R,C)$
having quantifier elimination and being universally axiomatizable. The
condition applies for example in the case when $C$ is a convex subring of an
o-minimal field $R$ and its residue field is o-minimal. |
|---|---|
| AbstractList | Let $R$ be an o-minimal expansion of a group in a language in which
$\textrm{Th}(R)$ eliminates quantifiers, and let $C$ be a predicate for a
valuational cut in $R$. We identify a condition that implies quantifier
elimination for $\textrm{Th}(R,C)$ in the language of $R$ expanded by $C$ and a
small number of constants, and which, in turn, is implied by $\textrm{Th}(R,C)$
having quantifier elimination and being universally axiomatizable. The
condition applies for example in the case when $C$ is a convex subring of an
o-minimal field $R$ and its residue field is o-minimal. |
| Author | Ealy, Clifton Maříková, Jana |
| Author_xml | – sequence: 1 givenname: Clifton surname: Ealy fullname: Ealy, Clifton – sequence: 2 givenname: Jana surname: Maříková fullname: Maříková, Jana |
| BackLink | https://doi.org/10.48550/arXiv.2006.08124$$DView paper in arXiv |
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| Snippet | Let $R$ be an o-minimal expansion of a group in a language in which
$\textrm{Th}(R)$ eliminates quantifiers, and let $C$ be a predicate for a
valuational cut... |
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| SubjectTerms | Mathematics - Logic |
| Title | Quantifier elimination for o-minimal structures expanded by a valuational cut |
| URI | https://arxiv.org/abs/2006.08124 |
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