scholarly journals Model theory of fields: An application to positive semidefinite polynomials

1984 ◽  
Vol 1 ◽  
pp. 53-65 ◽  
Author(s):  
Alexander Prestel
Keyword(s):  
Model Theory ◽  
Positive Semidefinite ◽  
Theory Of Fields ◽  
Model Theory Of Fields

Some model theory for almost real closed fields

1996 ◽  
Vol 61 (4) ◽  
pp. 1121-1152 ◽  
Author(s):  
Françoise Delon ◽  
Rafel Farré
Keyword(s):  
Model Theory ◽  
Residue Field ◽  
Elementary Equivalence ◽  
First Order ◽  
Valuation Rings ◽  
Closed Fields ◽  
Theory Of Fields ◽  
Model Theory Of Fields ◽  
Elementary Inclusion ◽  
Henselian Valuation

AbstractWe study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and prove that the definable real valuation rings of k are in correspondence with the definable convex subgroups of the value group of a certain real valuation of k.

Model Theory of Fields

2016 ◽  
Author(s):  
David Marker ◽  
Margit Messmer ◽  
Anand Pillay
Keyword(s):  
Model Theory ◽  
Theory Of Fields ◽  
Model Theory Of Fields

Model Theory of Fields

2005 ◽  
Author(s):  
David Marker ◽  
Margit Messmer ◽  
Anand Pillay
Keyword(s):  
Model Theory ◽  
Theory Of Fields ◽  
Model Theory Of Fields

Introduction to the Model Theory of Fields

2017 ◽  
pp. 1-37 ◽  
Author(s):  
David Marker ◽  
David Marker ◽  
Margit Messmer ◽  
Anand Pillay
Keyword(s):  
Model Theory ◽  
Theory Of Fields ◽  
Model Theory Of Fields

Diophantine Geometry from Model Theory

2001 ◽  
Vol 7 (1) ◽  
pp. 37-57 ◽  
Author(s):  
Thomas Scanlon
Keyword(s):  
Model Theory ◽  
Stability Theory ◽  
Function Field ◽  
Algebraic Groups ◽  
Diophantine Geometry ◽  
Diophantine Problems ◽  
Theory Of Fields ◽  
Model Theory Of Fields

Abstract§1. Introduction. With Hrushovski's proof of the function field Mordell-Lang conjecture [16] the relevance of geometric stability theory to diophantine geometry first came to light. A gulf between logicians and number theorists allowed for contradictory reactions. It has been asserted that Hrushovski's proof was simply an algebraic argument masked in the language of model theory. Another camp held that this theorem was merely a clever one-off. Still others regarded the argument as magical and asked whether such sorcery could unlock the secrets of a wide coterie of number theoretic problems.In the intervening years each of these prejudices has been revealed as false though such attitudes are still common. The methods pioneered in [16] have been extended and applied to a number of other problems. At their best, these methods have been integrated into the general methods for solving diophantine problems. Moreover, the newer work suggests limits to the application of model theory to diophantine geometry. For example, all such known applications are connected with commutative algebraic groups. This need not be an intrinsic restriction, but its removal requires serious advances in the model theory of fields.

scholarly journals Model theory of fields with free operators in positive characteristic

2019 ◽  
Vol 372 (8) ◽  
pp. 5991-6016
Author(s):  
Özlem Beyarslan ◽  
Daniel Max Hoffmann ◽  
Moshe Kamensky ◽  
Piotr Kowalski
Keyword(s):  
Model Theory ◽  
Positive Characteristic ◽  
Theory Of Fields ◽  
Model Theory Of Fields

Model Theory of Fields

1996 ◽  
Author(s):  
David Marker ◽  
Margit Messmer ◽  
Anand Pillay
Keyword(s):  
Model Theory ◽  
Theory Of Fields ◽  
Model Theory Of Fields
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