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pseudopiane

English translation: pseudoplane

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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
Italian term or phrase:pseudopiane
English translation:pseudoplane
Entered by: Peter Cox
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13:47 Jan 9, 2001
Italian to English translations [PRO]
Tech/Engineering
Italian term or phrase: pseudopiane
Nel campo delle strutture "pseudopiane"

In connection with prefabricated structures - this one is parabolic
Peter Cox
Italy
Local time: 11:03
pseudoplane
Explanation:
If the assumption that the geometry is locally finite is dropped, the author shows that every strongly minimal set falls into one of the above categories or contains a definable pseudoplane, a combinatorial configuration introduced by Lachlan in a different model-theoretic context. (Usually, classes (ii) and (iii) are combined in this context to form the class of module-like structures, so this is called the trichotomy theorem.) The author conjectured that those strongly minimal sets which interpret pseudoplanes are, roughly speaking, bi-interpretable with an algebraically closed field. This conjecture was refuted by Hrushovski. Hrushovski and the author have developed the class of Zariski structures---geometries with sufficient structure to recover the conjecture. This development displays intensive connections between model theory and algebraic geometry.
(http://www.cs.bgu.ac.il/~kojman/colloquium/zilberrev.html)
Selected response from:

Brigitte Gendebien
Belgium
Local time: 11:03
Grading comment
Wow! What an explanation. Thank you
4 KudoZ points were awarded for this answer

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Summary of answers provided
napseudoplane
Brigitte Gendebien


  

Answers


15 mins
pseudoplane


Explanation:
If the assumption that the geometry is locally finite is dropped, the author shows that every strongly minimal set falls into one of the above categories or contains a definable pseudoplane, a combinatorial configuration introduced by Lachlan in a different model-theoretic context. (Usually, classes (ii) and (iii) are combined in this context to form the class of module-like structures, so this is called the trichotomy theorem.) The author conjectured that those strongly minimal sets which interpret pseudoplanes are, roughly speaking, bi-interpretable with an algebraically closed field. This conjecture was refuted by Hrushovski. Hrushovski and the author have developed the class of Zariski structures---geometries with sufficient structure to recover the conjecture. This development displays intensive connections between model theory and algebraic geometry.
(http://www.cs.bgu.ac.il/~kojman/colloquium/zilberrev.html)



    Reference: http://www.zib.de/PaperWeb/abstracts/SC-91-10/
    Reference: http://www.cs.columbia.edu/~sanders/graphtheory/people/Borod...
Brigitte Gendebien
Belgium
Local time: 11:03
Native speaker of: Native in FrenchFrench
PRO pts in pair: 98
Grading comment
Wow! What an explanation. Thank you
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