Immediate expansions by valuation of fields

The main subject of investigation is the so-called “immediate expansion” phenomenon in various first-order valued-field structures over the corresponding underlying field structures. In particular, certain “valued o-minimal fields”, certain Henselian valued fields with non-divisible valued groups, and certain separably closed valued fields of finite imperfection degree, are shown to have this property.

[1]  Gregory L. Cherlin,et al.  Real closed rings II. model theory , 1983, Ann. Pure Appl. Log..

[2]  A. Wadsworth.  $p$-Henselian field: $K$-theory, Galois cohomology, and graded Witt rings. , 1983 .

[3]  Franziska Jahnke,et al.  DEFINABLE HENSELIAN VALUATIONS , 2012, The Journal of Symbolic Logic.

[4]  Anand Pillay,et al.  Reducts of (C, +, *) which Contain + , 1990, J. Symb. Log..

[5]  S. Lang.  Introduction to Algebraic Geometry , 1972 .

[6]  A. Wilkie.  TAME TOPOLOGY AND O-MINIMAL STRUCTURES (London Mathematical Society Lecture Note Series 248) By L OU VAN DEN D RIES : 180 pp., £24.95 (US$39.95, LMS Members' price £18.70), ISBN 0 521 59838 9 (Cambridge University Press, 1998). , 2000 .

[7]  Charles Steinhorn,et al.  Tame Topology and O-Minimal Structures , 2008 .

[8]  Angus Macintyre,et al.  Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields , 2013, Ann. Pure Appl. Log..

[9]  Dugald Macpherson,et al.  Weakly o-minimal structures and real closed fields , 2000 .

[10]  Ya'acov Peterzil,et al.  Additive reducts of real closed fields , 1992, Journal of Symbolic Logic (JSL).

[11]  P. Conrad.  Regularly ordered groups , 1962 .

[12]  J. Cassels.  Algebraic number theory , 2018, Graduate Studies in Mathematics.

[13]  Françoise Delon,et al.  Some model theory for almost real closed fields , 1996, Journal of Symbolic Logic.

[14]  J. W. S. Cassels,et al.  Algebraic number theory : proceedings of an instructional conference organized by the London Mathematical Society (a Nato Advanced Study Institute) with the support of the International Mathematical Union , 1967 .

[15]  Deirdre Haskell,et al.  A note on valuation definable expansions of fields , 1998, The Journal of Symbolic Logic.

[16]  Anand Pillay,et al.  Between Groups and rings , 1989 .

[17]  Martin Ziegler,et al.  Model theoretic methods in the theory of topological fields. , 1978 .

[18]  P. Conrad.  Extensions of ordered groups , 1955 .

[19]  Angus Macintyre,et al.  Logarithmic-exponential series , 2001, Ann. Pure Appl. Log..

[20]  Abraham Robinson,et al.  Elementary properties of ordered abelian groups , 1960 .

[21]  Model- and substructure complete theories of ordered Abelian groups , 1984 .

[22]  G. Fischer,et al.  Plane Algebraic Curves , 1921, Nature.

[23]  Gabriel Srour,et al.  The Independence Relation in Separably Closed Fields , 1986, J. Symb. Log..

[24]  Frank O. Wagner,et al.  Artin-Schreier extensions in NIP and simple fields , 2010, 1009.5421.

[25]  S. Kochen,et al.  Diophantine Problems Over Local Fields I , 1965 .

[26]  Françoise Delon,et al.  Idéaux et types sur les corps séparablement clos , 1988 .

[27]  C. Toffalori,et al.  A guide to classical and modern model theory , 2003 .