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Nonstandard Meromorphic Groups

2006
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Electronical Notes in Theoretical Computer Science
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Extending the work of [7] on

doi:10.1016/j.entcs.2005.05.029
fatcat:ps3vmwkzf5bs7bkbx2ahtus7hm
*groups*definable in compact complex manifolds and of [1] on strongly minimal*groups*definable in*nonstandard*compact complex manifolds, we classify all*groups*definable in ...*nonstandard*compact complex manifolds showing that if G is such a*group*then there are a linear algebraic*group*L, a definably compact*group*T , and definable exact sequence 1 → L → G → T → 1. ... holds for*groups*definable in*nonstandard*compact complex manifolds. ...##
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Strongly minimal groups in the theory of compact complex spaces

2006
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Journal of Symbolic Logic (JSL)
*

AbstractWe characterise strongly minimal

doi:10.2178/jsl/1146620157
fatcat:tkt4ka7aajgh3itky4brorhfd4
*groups*interpretable in elementary extensions of compact complex analytic spaces. ... Every*group*interpretable in A has the structure of a*nonstandard**meromorphic**group*. Proof. ... A*meromorphic**group*in A (or a*nonstandard**meromorphic**group*) is given by the following data: a definable*group*(G, +) in A with a finite covering by definable sets W 1 , . . . , W n ; and definable bijections ...##
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Page 2468 of Mathematical Reviews Vol. , Issue 97D
[page]

1997
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Mathematical Reviews
*

The last section discusses deformations of

*meromorphic*equations on P'(C). {For the entire collection see MR 96f:58002.} J. Dorfmeister (1-KS; Lawrence, KS) ... (RS-AOS-L; Moscow); Frenkel, Edward (1-HRV; Cambridge, MA) Integrals of motion and quantum*groups*. ...##
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Page 3839 of Mathematical Reviews Vol. , Issue 85i
[page]

1985
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Mathematical Reviews
*

[Algebraic properties of infinite products] Study

*group*on ultrametric analysis, 10th year: 1982/83, No. 1, Exp. No. 11, 14 pp., Inst. Henri Poincaré, Paris, 1984. ... The author shows that for every F € H(A/,) there exists F € H(A/))*meromorphic*in K, with only a simple pole at each 8, such that limjzj.1,2¢a, F(z) — F(z) =0. ...##
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Page 6653 of Mathematical Reviews Vol. , Issue 93m
[page]

1993
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Mathematical Reviews
*

However, the theory of quasitilings provides an adequate technique to extend the entropy formula to such

*group*actions. ... On the other hand, in important applications of*nonstandard*analysis, topological spaces appear which do not belong to the standard model; for example, the*nonstandard*hulls of topological vector spaces ...##
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Page 1994 of Mathematical Reviews Vol. , Issue 94d
[page]

1994
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Mathematical Reviews
*

The problems are

*grouped*into two chapters: Real analysis and Com- plex analysis. ... The author begins with a discussion of*nonstandard*analysis as a rare branch of pure mathematics where the thrust of current ...##
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Page 2000 of Mathematical Reviews Vol. , Issue 97M
[page]

1997
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Mathematical Reviews
*

No. 7 {of Séminaire d’Analyse, 1991-1992}, 15 pp.); Marie-Claude Sarmant [Marie-Claude Sarmant-Durix], Caractéres p-adiques d’un

*groupe*de produits*méromorphes*[p-adic characters of a*group*of*meromorphic*... No. 7, 23 pp.); Yvette Feneyrol-Perrin, Variations nonstan- dard sur le théoréme de Picard [*Nonstandard*variations on the Picard theorem] (Exp. ...##
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Page 4 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
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Mathematical Reviews
*

No. 6, 13 pp.); Abdelbaki Boutabaa, Décomposition de fonctions

*méromorphes*p-adiques [Decompo- sition of p-adic*meromorphic*functions] (Exp. ... Klimyk,*Nonstandard*U,(so3) and U,(so4): tensor products of representations, oscillator re- alizations and roots of unity (13-16); Michéle Irac-Astaud, A three-parameter deformation of the Weyl-Heisenberg ...##
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Page 3892 of Mathematical Reviews Vol. , Issue 87g
[page]

1987
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Mathematical Reviews
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The author continues his investigations on representations of sym-
metry

*groups*. ... The trick is to add some extra variables €1,°**»€, to consider some algebra A in {€;} (such as polyno- mials, analytic or*meromorphic*functions) and to define as basic objects finite linear combinations ...##
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Page 5287 of Mathematical Reviews Vol. , Issue 2002G
[page]

2002
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Mathematical Reviews
*

Standard single parameter g-deformation, various

*nonstandard*h-deformations, and hybrid (q,/)-deformations of GL(2) are ex- tensively studied. ... G.]| (BG-AOS-N; Sofia) On combined standard-*nonstandard*or hybrid (¢, /: )-deformations. (English summary) J. Math. Phys. 42 (2001), no. 3, 1236-1249. ...##
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Model theory of compact complex manifolds with an automorphism

2017
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Transactions of the American Mathematical Society
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Motivated by possible applications to

doi:10.1090/tran/6941
fatcat:4ft2kizkufhova3bn75gek4lpu
*meromorphic*dynamics, and generalising known properties of difference-closed fields, this paper studies the theory CCMA of compact complex manifolds with a generic ... [1, Definition 4.3] ; it is the natural*nonstandard*analogue of*meromorphic**group*. ... An A -compact*group*appears as the generic fibre of a definable family of*meromorphic**groups*that are individually, though not necessarily uniformly, definably isomorphic to complex tori. ...##
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Page 1257 of Mathematical Reviews Vol. , Issue 93c
[page]

1993
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Mathematical Reviews
*

In the present paper they study the form of w and the so- lutions y by putting them into the form of

*meromorphic*products. ... Summary: “We propose a systematic construction of examples of valued fields of generalized power series having value*group*and residue field with given prescribed properties.” 93¢:12014 12315 03C60 Delon ...##
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Page 2988 of Mathematical Reviews Vol. , Issue 97E
[page]

1997
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Mathematical Reviews
*

Using techniques of

*nonstandard*analysis, the author considers these phenomena for affine systems in one of the variables. ... Kluwer Academic Publishers*Group*, Dordrecht, 1996. xxii+-439 pp. $199.00. ISBN 0-7923-3940-1 This is a good textbook for beginning undergraduate courses in difference equations. ...##
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Page 546 of Mathematical Reviews Vol. , Issue 86b
[page]

1986
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Mathematical Reviews
*

They have been

*grouped*under several topic headings within which numbering has been consecutive since the first conference. ... Krieger (Heidelberg) 28E Miscellaneous topics Loeb, Peter A. (1-IL) 86b:28026 A functional approach to*nonstandard*measure theory. ...##
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Bounding nonminimality and a conjecture of Borovik-Cherlin
[article]

2021
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arXiv
*
pre-print

The Borovik-Cherlin conjecture itself is verified for algebraic and

arXiv:2106.02537v2
fatcat:6norwbr235axhajfkcbbyaqgxa
*meromorphic**group*actions, and a bound of U-rank plus 1 is then deduced unconditionally for differentially closed fields and compact ... In A ′ every*meromorphic**group*arises as a*nonstandard*fibre of a definable family of*meromorphic**groups*in the standard model. ... Finally, for (3) , we apply the*nonstandard*Chevellay-type structure theorem for*meromorphic**groups*in A ′ established in [2, 30] . ...
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