Analytic Zariski structures and the Hrushovski construction

NJ Peatfield; B Zilber

doi:10.1016/j.apal.2004.06.006

Analytic Zariski structures and the Hrushovski construction

NJ Peatfield, B Zilber

School of Mathematics

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4 Citations (Scopus)

Abstract

A set of axioms is presented defining an 'analytic Zariski structure', as a generalisation of Hrushovski and Zilber's Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski's method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of 'quasi-analytic' results are derived for this example e.g. analogues of Chow's theorem and the proper mapping theorem. (C) 2004 Elsevier B.V. All rights reserved.

Translated title of the contribution	Analytic Zariski structures and the Hrushovski construction
Original language	English
Pages (from-to)	127 - 180
Number of pages	54
Journal	Annals of Pure and Applied Logic
Volume	132 (2-3)
DOIs	https://doi.org/10.1016/j.apal.2004.06.006
Publication status	Published - Mar 2005

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Publisher: Elsevier
Other identifier: IDS Number: 886JV

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title = "Analytic Zariski structures and the Hrushovski construction",

abstract = "A set of axioms is presented defining an 'analytic Zariski structure', as a generalisation of Hrushovski and Zilber's Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski's method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of 'quasi-analytic' results are derived for this example e.g. analogues of Chow's theorem and the proper mapping theorem. (C) 2004 Elsevier B.V. All rights reserved.",

author = "NJ Peatfield and B Zilber",

note = "Publisher: Elsevier Other identifier: IDS Number: 886JV ",

year = "2005",

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doi = "10.1016/j.apal.2004.06.006",

language = "English",

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T1 - Analytic Zariski structures and the Hrushovski construction

AU - Peatfield, NJ

AU - Zilber, B

N1 - Publisher: Elsevier Other identifier: IDS Number: 886JV

PY - 2005/3

Y1 - 2005/3

N2 - A set of axioms is presented defining an 'analytic Zariski structure', as a generalisation of Hrushovski and Zilber's Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski's method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of 'quasi-analytic' results are derived for this example e.g. analogues of Chow's theorem and the proper mapping theorem. (C) 2004 Elsevier B.V. All rights reserved.

AB - A set of axioms is presented defining an 'analytic Zariski structure', as a generalisation of Hrushovski and Zilber's Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski's method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of 'quasi-analytic' results are derived for this example e.g. analogues of Chow's theorem and the proper mapping theorem. (C) 2004 Elsevier B.V. All rights reserved.

U2 - 10.1016/j.apal.2004.06.006

DO - 10.1016/j.apal.2004.06.006

M3 - Article (Academic Journal)

SN - 1873-2461

VL - 132 (2-3)

SP - 127

EP - 180

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

ER -

Analytic Zariski structures and the Hrushovski construction

Abstract

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