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Imaginaries in dense pairs of real-closed fields
ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important role in model theory. In this thesis, we are interested in imaginaries of dense pairs of real-closed fields. More precisely, we consider the following problem: is acleq equal to dcleq in dense pairs of real-...
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2017
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| Summary: | ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important
role in model theory. In this thesis, we are interested in imaginaries of
dense pairs of real-closed fields. More precisely, we consider the following
problem: is acleq equal to dcleq in dense pairs of real-closed fields?
To answer this question, we first present some results about real-closed
fields, which are basically completeness, quantifier elimination and elimination
of imaginaries. Then, we concentrate on the completeness and near
model-completeness for the theory of dense pairs of real-closed fields. And
finally, we present the key point of the thesis. Namely, we demonstrate that
acleq(∅) = dcleq(∅) but there exists A such that acleq(A) 6= dcleq(A) |
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