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Some (non-)elimination results for curves in geometric structures

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Randriambololona S., Starchenko S.

Fundamenta Mathematicae

2011

tom 214

nr 2

181-198

We show that the first order structure whose underlying universe is ℂ and whose basic relations are all algebraic subsets of ℂ² does not have quantifier elimination. Since an algebraic subset of ℂ² is either of dimension ≤ 1 or has a complement of dimension ≤ 1, one can restate the former result as a failure of quantifier elimination for planar complex algebraic curves. We then prove that removing the planarity hypothesis suffices to recover quantifier elimination: the structure with the universe ℂ and a predicate for each algebraic subset of ℂⁿ of dimension ≤ 1 has quantifier elimination.

K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds

100%

Moosa R., Starchenko S.

Fundamenta Mathematicae

2008

tom 198

nr 2

139-148

It is shown that in an elementary extension of a compact complex manifold M, the K-analytic sets (where K is the algebraic closure of the underlying real closed field) agree with the ccm-analytic sets if and only if M is essentially saturated. In particular, this is the case for compact Kähler manifolds.

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2 Fundamenta Mathematicae

2 Starchenko S.

1 Moosa R.

1 Randriambololona S.

1 2011

1 2008

Wyniki wyszukiwania

Some (non-)elimination results for curves in geometric structures

K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds