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Nonstandard Meromorphic Groups

Thomas Scanlon
2006 Electronical Notes in Theoretical Computer Science  
Extending the work of [7] on 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.  ... 
doi:10.1016/j.entcs.2005.05.029 fatcat:ps3vmwkzf5bs7bkbx2ahtus7hm

Strongly minimal groups in the theory of compact complex spaces

Matthias Aschenbrenner, Rahim Moosa, Thomas Scanlon
2006 Journal of Symbolic Logic (JSL)  
AbstractWe characterise strongly minimal 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  ... 
doi:10.2178/jsl/1146620157 fatcat:tkt4ka7aajgh3itky4brorhfd4

Page 2468 of Mathematical Reviews Vol. , Issue 97D [page]

1997 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.  ... 

Page 3839 of Mathematical Reviews Vol. , Issue 85i [page]

1985 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.  ... 

Page 6653 of Mathematical Reviews Vol. , Issue 93m [page]

1993 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  ... 

Page 1994 of Mathematical Reviews Vol. , Issue 94d [page]

1994 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  ... 

Page 2000 of Mathematical Reviews Vol. , Issue 97M [page]

1997 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.  ... 

Page 4 of Mathematical Reviews Vol. , Issue 98A [page]

1998 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  ... 

Page 3892 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
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  ... 

Page 5287 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 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.  ... 

Model theory of compact complex manifolds with an automorphism

Martin Bays, Martin Hils, Rahim Moosa
2017 Transactions of the American Mathematical Society  
Motivated by possible applications to 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.  ... 
doi:10.1090/tran/6941 fatcat:4ft2kizkufhova3bn75gek4lpu

Page 1257 of Mathematical Reviews Vol. , Issue 93c [page]

1993 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  ... 

Page 2988 of Mathematical Reviews Vol. , Issue 97E [page]

1997 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.  ... 

Page 546 of Mathematical Reviews Vol. , Issue 86b [page]

1986 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.  ... 

Bounding nonminimality and a conjecture of Borovik-Cherlin [article]

James Freitag, Rahim Moosa
2021 arXiv   pre-print
The Borovik-Cherlin conjecture itself is verified for algebraic and 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] .  ... 
arXiv:2106.02537v2 fatcat:6norwbr235axhajfkcbbyaqgxa
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