Some model theory of simple algebraic groups over algebraically closed fields
B. I. Zilber (1984)
Colloquium Mathematicae
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B. I. Zilber (1984)
Colloquium Mathematicae
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Daniel Palacín, Frank O. Wagner (2014)
Fundamenta Mathematicae
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We prove a version of Hrushovski's Socle Lemma for rigid groups in an arbitrary simple theory.
Zhan Chen (2015)
Molecular Based Mathematical Biology
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Differential geometry (DG) based solvation models have shown their great success in solvation analysis by avoiding the use of ad hoc surface definitions, coupling the polar and nonpolar free energies, and generating solvent-solute boundary in a physically self-consistent fashion. Parameter optimization is a key factor for their accuracy, predictive ability of solvation free energies, and other applications. Recently, a series of efforts have been made to improve the parameterization...
Sy-David Friedman (2016)
Fundamenta Mathematicae
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In the author's 2012 paper, the V-definable Stable Core 𝕊 = (L[S],S) was introduced. It was shown that V is generic over 𝕊 (for 𝕊-definable dense classes), each V-definable club contains an 𝕊-definable club, and the same holds with 𝕊 replaced by (HOD,S), where HOD denotes Gödel's inner model of hereditarily ordinal-definable sets. In the present article we extend this to models of class theory by introducing the V-definable Enriched Stable Core 𝕊* = (L[S*],S*). As an application...
Slavik Jablan (2002)
Visual Mathematics
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Mário J. Edmundo, G. Terzo (2011)
Fundamenta Mathematicae
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We generalize the theory of generic subsets of definably compact definable groups to arbitrary o-minimal structures. This theory is a crucial part of the solution to Pillay's conjecture connecting definably compact definable groups with Lie groups.
J. Łoś (1955)
Fundamenta Mathematicae
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G. Cherlin (1979)
Fundamenta Mathematicae
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Siegfried Bosch, Klaus Schlöter (1995)
Mathematische Annalen
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Dov Gabbay (1977)
Fundamenta Mathematicae
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Ludomir Newelski (2003)
Open Mathematics
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Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.
Žarko Mijajlović (1977)
Zbornik Radova
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Akito Tsuboi (2009)
Colloquium Mathematicae
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Let p(x) be a nonprincipal type. We give a sufficient condition for a model M to have a proper elementary extension omitting p(x). As a corollary, we obtain a generalization of Steinhorn's omitting types theorem to the supersimple case.
Johannes Walcher (2011)
Annales de l’institut Fourier
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In recent years, mirror symmetry for open strings has exhibited some new connections between symplectic and enumerative geometry (A-model) and complex algebraic geometry (B-model) that in a sense lie between classical and homological mirror symmetry. I review the rôle played in this story by matrix factorizations and the Calabi-Yau/Landau-Ginzburg correspondence.