scholarly journals On definable Galois groups and the strong canonical base property

2017 ◽  
Vol 17 (01) ◽  
pp. 1750002
Author(s):  
Daniel Palacín ◽  
Anand Pillay
Keyword(s):  
Finite Rank ◽  
Galois Groups ◽  
Strong Form ◽  
Current Paper ◽  
Base Property ◽  
Canonical Base ◽  
Definition Of

In [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. (N.S.) 19(4) (2013) 865–877], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that [Formula: see text] has the canonical base property in a strong form; “internality to” being replaced by “algebraicity in”. In the current paper, we give a reasonably robust definition of the “strong canonical base property” in a rather more general finite rank context than [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. (N.S.) 19(4) (2013) 865–877], and prove its equivalence with rigidity of the relevant definable Galois groups. The new direction is an elaboration on the old result that [Formula: see text]-based groups are rigid.

scholarly journals On Near-Rings of Quotients

1979 ◽  
Vol 22 (2) ◽  
pp. 77-86 ◽  
Author(s):  
A. Oswald
Keyword(s):  
Finite Rank ◽  
Minimum Condition ◽  
Suitable Definition ◽  
Definition Of ◽  
Rings Of Quotients

In (2), Holcombe investigated near-rings of zero-preserving mappings of a group Γ which commute with the elements of a semigroup S of endomorphisms of Γ and examined the question: under what conditions do near-rings of this type have near-rings of right quotients which are 2-primitive with minimum condition on right ideals? In the first part of this paper (§2) we investigate further properties of near-rings of this type. The second part of the paper (§3) deals with those near-rings which have semisimple near-rings of right quotients. Our results here are analogous to those of Goldie (1); in particular, with a suitable definition of finite rank we prove that a near-ring which has a semisimple near-ring of right quotients has finite rank

scholarly journals CONSTRUCTING TYPES IN DIFFERENTIALLY CLOSED FIELDS THAT ARE ANALYSABLE IN THE CONSTANTS

2018 ◽  
Vol 83 (04) ◽  
pp. 1413-1433
Author(s):  
RUIZHANG JIN
Keyword(s):  
Minimal Length ◽  
Canonical Analysis ◽  
Base Property ◽  
Canonical Base ◽  
Closed Fields ◽  
Image Position ◽  
Positive Integers

AbstractAnalysability of finiteU-rank types are explored both in general and in the theory${\rm{DC}}{{\rm{F}}_0}$. The well-known fact that the equation$\delta \left( {{\rm{log}}\,\delta x} \right) = 0$is analysable in but not almost internal to the constants is generalized to show that$\underbrace {{\rm{log}}\,\delta \cdots {\rm{log}}\,\delta }_nx = 0$is not analysable in the constants in$\left( {n - 1} \right)$-steps. The notion of acanonical analysisis introduced–-namely an analysis that is of minimal length and interalgebraic with every other analysis of that length. Not every analysable type admits a canonical analysis. Using properties of reductions and coreductions in theories with the canonical base property, it is constructed, for any sequence of positive integers$\left( {{n_1}, \ldots ,{n_\ell }} \right)$, a type in${\rm{DC}}{{\rm{F}}_0}$that admits a canonical analysis with the property that theith step hasU-rank${n_i}$.

scholarly journals Towards a semiotic definition of trash

2001 ◽  
Vol 29 (1) ◽  
pp. 313-324
Author(s):  
Riste Keskpaik
Keyword(s):  
Structural Similarity ◽  
Current Paper ◽  
Environmental Crisis ◽  
Theoretical Literature ◽  
Semiotic Approach ◽  
New Perspective ◽  
Definition Of

The phenomenon of trash has rarely been addressed in the cultural theoretical literature. However, its structural similarity with the concept of taboo as well as its role in the dynamics of culture has been stated. Current paper aims to summarize the partial contributions that have been made so far, localize them in a larger semiotic framework, and deriving from Lonnan's approach to culture suggest a few further ideas for a semiotic definition of trash. It is proposed to define trash as a phenomenon marking the boundary between culhlre and non-culture/nature. In the context of the deepening environmental crisis (to which accumulation of trash contributes) a semiotic approach opens a new perspective for identifying the origin of the problem in our mind/culture rather than in nature.

scholarly journals An Integrative Definition of Coaching Effectiveness and Expertise

2009 ◽  
Vol 4 (3) ◽  
pp. 307-323 ◽  
Author(s):  
Jean Côté ◽  
Wade Gilbert
Keyword(s):  
Positive Psychology ◽  
Final Section ◽  
Conceptual Models ◽  
Current Paper ◽  
Definition Of ◽  
Development Literature ◽  
Coaching Effectiveness ◽  
Three Components

The purpose of the current paper is to present an integrative definition of coaching effectiveness and expertise that is both specific and conceptually grounded in the coaching, teaching, positive psychology, and athletes' development literature. The article is organized into six sections. The first section is used to situate the proposed definition in the predominant conceptual models of coaching. The second, third, and fourth sections provide detailed discussion about each of the three components of the proposed definition of coaching effectiveness: (a) coaches' knowledge, (b) athletes' outcomes, and (c) coaching contexts. The proposed definition is presented in the fifth section along with a clarification of common terminology and guiding postulates. The final section includes implications for practice and research.

scholarly journals Ample thoughts

2013 ◽  
Vol 78 (2) ◽  
pp. 489-510 ◽  
Author(s):  
Daniel Palacín ◽  
Frank O. Wagner
Keyword(s):  
General Notion ◽  
Base Property ◽  
Simple Theories ◽  
Canonical Base ◽  
Weakened Version ◽  
Special Case

AbstractNon-n-ampleness as denned by Pillay [20] and Evans [5] is preserved under analysability. Generalizing this to a more general notion of Σ-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis [4] for types of finite SU-rank. This is then applied to the special case of groups.

Plus ultra

2015 ◽  
Vol 15 (02) ◽  
pp. 1550008
Author(s):  
Frank O. Wagner
Keyword(s):  
Equivalence Relations ◽  
Base Property ◽  
Canonical Base

We define a reasonably well-behaved class of ultraimaginaries, i.e. classes modulo [Formula: see text]-invariant equivalence relations, called tame, and establish some basic simplicity-theoretic facts. We also show feeble elimination of supersimple ultraimaginaries: If [Formula: see text] is an ultraimaginary definable over a tuple [Formula: see text] with [Formula: see text], then [Formula: see text] is eliminable up to rank [Formula: see text]. Finally, we prove some uniform versions of the weak canonical base property.

scholarly journals Actions of finite rank: weak rational ergodicity and partial rigidity

2015 ◽  
Vol 36 (7) ◽  
pp. 2138-2171 ◽  
Author(s):  
ALEXANDRE I. DANILENKO
Keyword(s):  
Simple Proof ◽  
Finite Rank ◽  
Abelian Groups ◽  
Interval Exchange ◽  
Infinite Measure ◽  
Interval Exchange Transformations ◽  
Bratteli Diagrams ◽  
Rank One ◽  
Partial Rigidity ◽  
Definition Of

A simple proof of the fact that each rank-one infinite measure preserving (i.m.p.) transformation is subsequence weakly rationally ergodic is found. Some classes of funny rank-one i.m.p. actions of Abelian groups are shown to be subsequence weakly rationally ergodic. A constructive definition of finite funny rank for actions of arbitrary infinite countable groups is given. It is shown that the ergodic i.m.p. transformations of balanced finite funny rank are subsequence weakly rationally ergodic. It is shown that the ergodic probability preserving transformations of exact finite rank, the ergodic Bratteli–Vershik maps corresponding to the ‘consecutively ordered’ Bratteli diagrams of finite rank, some their generalizations and the ergodic interval exchange transformations are partially rigid.

scholarly journals On the canonical base property

2013 ◽  
Vol 19 (4) ◽  
pp. 865-877 ◽  
Author(s):  
Ehud Hrushovski ◽  
Daniel Palacín ◽  
Anand Pillay
Keyword(s):  
Base Property ◽  
Canonical Base

scholarly journals Concept of Abetment in the IPC (2013)

2017 ◽  
Vol 10 (2) ◽  
pp. 162
Author(s):  
Mahmood Rooholamini
Keyword(s):  
Criminal Law ◽  
Penal Code ◽  
Current Paper ◽  
Legal Term ◽  
Legal Perspective ◽  
Significant Difference ◽  
Definition Of

Undoubtedly, in many cases, the definition of a legal term or an entity provided by lawyers has significant difference with the definition provided by the institution of the legislature. Therefore, it can be distinguished between the concept of abbeting from a legal perspective, i.e., from the perspective of lawyers and the legal perspective as well as that of the legislature. There is no single definition of abetment from a legal standpoint, but there are various definitions of the term. However, the definitions have much in common. Iranian legislator has not defined “abetment” in the Islamic Penal Code (2003) but addressed some cases of behaviors that may constitute complicity in the crime. In addition, the Iranian legislator has extended the scope of the crimes that shall also apply abetment in IPC (2013). This is contrary to the principle of minimumality of criminal law based on the scope of the criminal law must be limited. In addition, the new law has serious flaws that have the current paper tried to remind objections and provide recommendations for amendments.

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