Model theory

By David Marker. 2002

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Sato–Tate theorem for families and low-lying zeros of automorphic $$L$$L-functions (2012, unknown): “[73]).”
Homogeneity and prime models in torsion-free hyperbolic groups (2010, background): “For further notions of homogeneity, we refer the reader to [8, 14].”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “We briefly recall some definitions here and refer to [90] for details.”
On algebraic relations between solutions of a generic Painleve equation (2011, background): “Thanks also to Frank Nijhoff and Davide Penazzi for numerous discussions related to the material presented here.”
Extending partial isometries (2005, background): “For model theoretic notation and terminology the reader may consult the first section of [7].”
Unification theorems in algebraic geometry (2008, methodology): “Recall (see, for example, [32]), that a type in variables X of L over T is a consistent with T set p of formulas in Φ L ( X ), i.e, a subset p ⊆ Φ L ( X ) that can be realized in a structure from Mod( T ).”
Constructible motivic functions and motivic integration (2004, background): “In particular, only basic familiarity with the first chapters of textbooks like those of Hartshorne [20] and Marker [25] is required.”
Stable group theory and approximate subgroups (2009, background): “We refer to the reader to a book such as [4], [34] or the lecture notes in [38] for a fuller treatment.”