540 research outputs found
Uniformly locally o-minimal open core
This paper discusses sufficient conditions for a definably complete densely
linearly ordered expansion of an abelian group having the uniformly locally
o-minimal open cores of the first/second kind and strongly locally o-minimal
open core, respectively
Sedimentary facies of the Tetori Group in the Shiramine, Ishikawa Prefecture
The Mesozoic Tetori Group, exposed in the Shiramine area of Ishikawa Prefecture, is characterized by nonmarine deposits unconformably overlying the Hida Metamorphic Rocks. Sedimentological investigation of the upper part of the Akaiwa Formation (the upper part of the Tetori Group) recognized seven sedimentary facies (channel floor, sand bar, plane beds, crevasse splay, flood plain, vegetated swamp, and soil) and seven cycles; each of them generally appears fining upwards.
Stratigraphy of the upper part of the Akaiwa Formation shows a graded change from a gravely fluvial system (the lowest cycle) to a sandy meandering river system (the upper cycles). Nodular calcretes found from the soil facies indicate that the climate was once arid during sedimentation of the upper part of the Akaiwa Formation. However, it is inconsistent with well development of coal seams and carbonaceous mudstone
Expansion of a semi-bounded o-minimal structure by a geometric progression
We demonstrate that an expansion of a semi-bounded o-minimal expansion of the
ordered group of reals by an increasing geometric progression is locally
o-minimal
Definable quotients in d-minimal structures
We consider d-minimal expansions of ordered fields. We demonstrate the
existence of definable quotients of definable sets by definable equivalence
relations when several technical conditions are satisfied. These conditions are
satisfied when there is a definable proper action of a definable group on a
locally closed definable subset of , where is the universe.Comment: arXiv admin note: substantial text overlap with arXiv:2212.0640
Almost o-minimal structures and -structures
We propose new structures called almost o-minimal structures and -structures. The former is a first-order expansion of a dense linear order
without endpoints such that the intersection of a definable set with a bounded
open interval is a finite union of points and open intervals. The latter is a
variant of van den Dries and Miller's analytic geometric categories and
Shiota's -sets and -sets. In them, the family of
definable sets are closed only under proper projections unlike first-order
structures. We demonstrate that an -expansion of an ordered
divisible abelian group always contains an o-minimal expansion of an ordered
group such that all bounded -definable sets are definable in the
structure.
Another contribution of this paper is a uniform local definable cell
decomposition theorem for almost o-minimal expansions of ordered groups
. Let be a
finite family of definable subsets of . Take an arbitrary positive
element and set . Then, there exists a finite partition
into definable sets \begin{equation*} M^m \times B = X_1 \cup \ldots \cup X_k
\end{equation*} such that is a definable
cell decomposition of for any and either or for any and . Here, the notation denotes the fiber of a definable subset
of at . We introduce the notion of multi-cells and
demonstrate that any definable set is a finite union of multi-cells in the
course of the proof of the above theorem.Comment: arXiv admin note: text overlap with arXiv:1912.0578
Notes on definably complete locally o-minimal expansions of ordered groups
We study definably complete locally o-minimal expansions of ordered groups in
this paper. A definable continuous function defined on a closed, bounded and
definable set behave like a continuous function on a compact set. We
demonstrate uniform continuity of a definable continuous function on a closed,
bounded and definable set and Arzela-Ascoli-type theorem. We propose a notion
of special submanifolds with tubular neighborhoods and show that any definable
set is decomposed into finitely many special submanifolds with tubular
neighborhoods.Comment: arXiv admin note: text overlap with arXiv:2010.0242
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