Maximal small extensions of o-minimal structures
نویسندگان
چکیده
منابع مشابه
Maximal small extensions of o-minimal structures
A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is possible to have an o-minimal structure with a maximal small extension. Our construction yields such a structure for any cardinality. We show that in some cases, notably when the base structure is countable, the maximal s...
متن کاملPeano Differentiable Extensions in O-minimal Structures
Peano differentiability generalizes ordinary differentiability to higher order. There are two ways to define Peano differentiability for functions defined on non-open sets. For both concepts, we investigate the question under which conditions a function defined on a closed set can be extended to a Peano differentiable function on the ambient space if the sets and functions are definable in an o...
متن کاملDefinable group extensions in semi-bounded o-minimal structures
In this note we show: Let R = 〈R, <, +, 0, . . . 〉 be a semi-bounded (respectively, linear) o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m ([Ed1]). Then G is a definable extension of a bounded (respectively, definably compact) definable group B by 〈Rm, +〉.
متن کاملFusing o-minimal structures
In this note I construct a proper o-minimal expansion of the ordered additive group of rationals.
متن کاملLocally o-minimal structures
In this paper we study (strongly) locally o-minimal structures. We first give a characterization of the strong local o-minimality. We also investigate locally o-minimal expansions of (R,+, <).
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: Mathematical Logic Quarterly
سال: 2010
ISSN: 0942-5616
DOI: 10.1002/malq.200910102