Heirs of box types in polynomially bounded structures
نویسندگان
چکیده
منابع مشابه
Heirs of box types in polynomially bounded structures
We characterize heirs of so called box types of a polynomially bounded o-minimal structure M . A box type is an n-type of M which is uniquely determined by the projections to the coordinate axes. From this, we deduce various structure theorems for subsets of M, definable in the expansion M of M by all convex subsets of the line. Moreover we obtain a model completeness result for M .
متن کاملLocally polynomially bounded structures
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally definable in a fixed o-minimal and polynomially bounded reduct. As an application we show that in certain o-minimal structures definable functions are piecewise im...
متن کاملPluriregularity in Polynomially Bounded O–minimal Structures
Given a polynomially bounded o–minimal structure S and a set A ⊂ R belonging to S, we show that A (considered as a subset of C) is pluriregular at every point a ∈ intA that can be attained by a C∞ arc γ : [0, ] → R belonging to S, such that γ(0) = a and γ((0, ]) ⊂ intA. In particular, if S is a recently found in [22] polynomially bounded o–minimal structure of quasianalytic functions in the sen...
متن کاملThe elementary theory of Dedekind cuts in polynomially bounded structures
Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M . We determine the first order theory of the structure M expanded by the set C. We do this also over any given set of parameters from M , which yields a description of all subsets of M, definable in the expanded structure. 1. Int...
متن کاملInfinitely Peano differentiable functions in polynomially bounded o-minimal structures
Let R be an o-minimal expansion of a real closed field. We show that the definable infinitely Peano differentiable functions are smooth if and only if R is polynomially bounded.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2009
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1254748689