scholarly journals Definable quotients of locally definable groups

2012 ◽  
Vol 18 (4) ◽  
pp. 885-903 ◽  
Author(s):  
Pantelis E. Eleftheriou ◽  
Ya’acov Peterzil
Keyword(s):  
Definable Groups ◽  
Locally Definable Groups ◽  
Definable Quotients

scholarly journals Locally definable subgroups of semialgebraic groups

2019 ◽  
Vol 20 (02) ◽  
pp. 2050009
Author(s):  
Elías Baro ◽  
Pantelis E. Eleftheriou ◽  
Ya’acov Peterzil
Keyword(s):  
Real Closed Field ◽  
Closed Field ◽  
Definable Groups ◽  
Locally Definable Groups ◽  
Semialgebraic Subset ◽  
Generic Set ◽  
Definable Quotients

We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. (N.S.) 18(4) (2012) 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds when [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text].

scholarly journals Discrete subgroups of locally definable groups

2013 ◽  
Vol 19 (3) ◽  
pp. 719-736 ◽  
Author(s):  
Alessandro Berarducci ◽  
Mário Edmundo ◽  
Marcello Mamino
Keyword(s):  
Discrete Subgroups ◽  
Definable Groups ◽  
Locally Definable Groups

Towards a More Competitive Mobile Payment Industry: Standardization And Beyond

2020 ◽  
Author(s):  
Xingyu Yan
Keyword(s):  
Financial Market ◽  
Competitive Dynamics ◽  
Mobile Payment ◽  
Market Failures ◽  
Mobile Payments ◽  
The World ◽  
Chinese Industry ◽  
Definable Groups ◽  
Study Case ◽  
Bank Card

Abstract Mobile payments are becoming increasingly popular around the world. In countries like China, they appear in the form of barcode payments and are poised to replace cash and bank card payments for day-to-day consumer purchases. Against that backdrop, this paper analyzes the availability of barcode standardization as an approach to interoperability and ultimately to enhanced competition in the mobile payment industry. It uses the Chinese industry as a study case, which features a duopoly structure and shifting competitive dynamics among three definable groups of market players. This paper confirms that standardization can enhance competition and argues that, in this case, a government-mandated standardization is preferable to a voluntary one because the latter is prone to financial market failures. Along this line, this paper makes three suggestions for furthering the barcode standardization. It also advises prudence and competitive neutrality for the financial regulator and calls for more active involvements of the competition and data protection authorities.

The Biology of the Gecko Oedura reticulata Bustard, in a Smal Habitat Isolate in the Western Australian Wheatbelt

1983 ◽  
Vol 10 (3) ◽  
pp. 543 ◽  
Author(s):  
RA How ◽  
DJ Kitchner
Keyword(s):  
Dead Wood ◽  
Life History Strategy ◽  
Late Summer ◽  
Native Vegetation ◽  
Body Temperatures ◽  
Ambient Temperatures ◽  
Slight Excess ◽  
Definable Groups ◽  
Eucalypt Woodland ◽  
Western Australian

The arboreal gecko Oedura reticulata was studied in an isolated 1-ha eucalypt woodland in the Western Australian wheatbelt. Females reach maturity in their 4th year and lay two eggs between October and January. Males reach maturity in their 3rd year, their testes are largest between July and October. Young hatch in mid to late summer but immature individuals are infrequently captured during their first 18 months. Individuals live more than 6 years. Population size ranged between 91 and 119 individuals. Individuals were placed into eight definable groups. There was a slight excess of males in each cohort. Activity, which is greatest in summer and least in winter, is closely correlated with ambient temperature. Body temperatures become noticeably higher than ambient temperatures between 23�C and 16�C; below 16�C activity is greatly reduced. The higher numbers of O.reticulata occur on mature smooth-barked eucalypt trees that have both large areas of foliage and dead wood. Only immature individuals frequently occupy rough-barked eucalypts. Their life-history strategy is considered in respect of small, isolated and disturbed remnants of native vegetation.

Definability and definable groups in simple theories

1998 ◽  
Vol 63 (3) ◽  
pp. 788-796 ◽  
Author(s):  
Anand Pillay
Keyword(s):  
Simple Theories ◽  
Definable Groups ◽  
The Right

AbstractWe continue the study of simple theories begun in [3] and [5]. We first find the right analogue of definability of types. We then develop the theory of generic types and stabilizers for groups definable in simple theories. The general ideology is that the role of formulas (or definability) in stable theories is replaced by partial types (or ∞-definability) in simple theories.

TYPE-DEFINABILITY, COMPACT LIE GROUPS, AND o-MINIMALITY

2004 ◽  
Vol 04 (02) ◽  
pp. 147-162 ◽  
Author(s):  
ANAND PILLAY
Keyword(s):  
Compact Lie Group ◽  
Compact Lie Groups ◽  
First Order ◽  
Special Cases ◽  
Definable Groups ◽  
Small Index ◽  
Logic Topology ◽  
The Right ◽  
Study Type ◽  
Order Structures

We study type-definable subgroups of small index in definable groups, and the structure on the quotient, in first order structures. We raise some conjectures in the case where the ambient structure is o-minimal. The gist is that in this o-minimal case, any definable group G should have a smallest type-definable subgroup of bounded index, and that the quotient, when equipped with the logic topology, should be a compact Lie group of the "right" dimension. I give positive answers to the conjectures in the special cases when G is 1-dimensional, and when G is definably simple.

Definable groups and compact p -adic Lie groups

2008 ◽  
Vol 78 (1) ◽  
pp. 233-247 ◽  
Author(s):  
A. Onshuus ◽  
A. Pillay
Keyword(s):  
Lie Groups ◽  
Definable Groups

scholarly journals Definability of groups in ℵ0-stable metric structures

2010 ◽  
Vol 75 (3) ◽  
pp. 817-840 ◽  
Author(s):  
Itaï Ben Yaacov
Keyword(s):  
Group Action ◽  
Stable Theory ◽  
Translation Invariant ◽  
Definable Groups ◽  
Metric Structures

AbstractWe prove that in a continuous ℵ0-stable theory every type-definable group is definable. The two main ingredients in the proof are:(i) Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from [Ben08], allowing us to prove the theorem in case the metric is invariant under the group action; and(ii) Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones.

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