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Towards a Model Theory of Almost Com...

Wan, Michael Wing Hei.

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Towards a Model Theory of Almost Complex Manifolds.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Towards a Model Theory of Almost Complex Manifolds./
Author:	Wan, Michael Wing Hei.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
Description:	66 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: A.
Contained By:	Dissertation Abstracts International78-11A(E).
Subject:	Logic. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10280380
ISBN:	9780355033113

Towards a Model Theory of Almost Complex Manifolds.
Wan, Michael Wing Hei.

Towards a Model Theory of Almost Complex Manifolds. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 66 p.

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: A.

Thesis (Ph.D.)--University of California, Berkeley, 2017.

We develop notions of "almost complex analytic subsets" of almost complex manifolds, modelled after complex analytic subsets of complex manifolds. Basic analytic-geometric results are presented, including an identity principle for almost complex maps, and a proof that the singular locus of an almost complex analytic set is itself an "equational" almost complex analytic set, under certain conditions.

ISBN: 9780355033113Subjects--Topical Terms:

529544
Logic.

Towards a Model Theory of Almost Complex Manifolds.
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020 $a 9780355033113
035 $a (MiAaPQ)AAI10280380
035 $a (MiAaPQ)berkeley:16886
035 $a AAI10280380
040 $a MiAaPQ $c MiAaPQ
100 1 $a Wan, Michael Wing Hei. $3 3343162
245 1 0 $a Towards a Model Theory of Almost Complex Manifolds.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 66 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: A.
500 $a Adviser: Thomas Scanlon.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2017.
520 $a We develop notions of "almost complex analytic subsets" of almost complex manifolds, modelled after complex analytic subsets of complex manifolds. Basic analytic-geometric results are presented, including an identity principle for almost complex maps, and a proof that the singular locus of an almost complex analytic set is itself an "equational" almost complex analytic set, under certain conditions.
520 $a This work is partly motivated by geometric model theory. B. Zilber observed that a compact complex manifold, equipped with the logico-topological structure given by its complex analytic subsets, satisfies the axioms for a so-called "Zariski geometry", kick-starting a fruitful model-theoretic study of complex manifolds. Our results point towards a natural generalization of Zilber's theorem to almost complex manifolds, using our notions of almost complex analytic subset. We include a discussion of progress towards this goal.
520 $a Our development draws inspiration from Y. Peterzil and S. Starchenko's theory of nonstandard complex analytic geometry. We work primarily in the real analytic setting.
590 $a School code: 0028.
650 4 $a Logic. $3 529544
650 4 $a Mathematics. $3 515831
690 $a 0395
690 $a 0405
710 2 $a University of California, Berkeley. $b Logic and the Methodology of Science. $3 3343163
773 0 $t Dissertation Abstracts International $g 78-11A(E).
790 $a 0028
791 $a Ph.D.
792 $a 2017
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10280380