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Switch to: References
Citations of:
Imaginaries in real closed valued fields
Annals of Pure and Applied Logic 139 (1):230-279 (2006)
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We consider the extent to which certain properties of definably complete structures may persist in structures which are not definably complete, particularly in the weakly o-minimal structures. |
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Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two transfer results, one on the VC-density and the other one, on the combinatorial property NTP2. |
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Model theorists have been studying analytic functions since the late 1970s. Highlights include the seminal work of Denef and van den Dries on the theory of the p-adics with restricted analytic functions, Wilkie's proof of o-minimality of the theory of the reals with the exponential function, and the formulation of Zilber's conjecture for the complex exponential. My goal in this talk is to survey these main developments and to reflect on today's open problems, in particular for theories of valued fields. |
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Let (K, v) be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. The main step in obtaining this partition is an answer to the question, given a polynomial f(x) ∈ K[x], what is v(f(x))? Two applications are given: first, a constructive quantifier elimination relative to the leading (...) |
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We initiate a geometric stability study of groups of the form G/G00, where G is a 1-dimensional definably compact, definably connected, definable group in a real closed field M. We consider an enriched structure M′ with a predicate for G00 and check 1-basedness or non-1-basedness for G/G00, where G is an additive truncation of M, a multiplicative truncation of M, SO2(M) or one of its truncations; such groups G/G00 are now interpretable in M′. We prove that the only 1-based groups (...) |
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We give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the ‘geometric' sorts which suffice to code all imaginaries in the corresponding algebraic setting. |
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We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes... |
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