On one-based theories

1994 ◽  
Vol 59 (2) ◽  
pp. 579-595 ◽  
Author(s):  
E. Bouscaren ◽  
E. Hrushovski
Keyword(s):  
Similar Type ◽  
Stable Theory ◽  
Dependence Relation ◽  
Regular Type

We know from [H1], [H2] that in a stable theory, given a nontrivial locally modular regular type q, one can define a group with generic domination equivalent to q, and that the dependence relation on q can be analyzed in terms of this group. In a stable one-based theory, every regular type is locally modular; hence, this result holds for every nontrivial regular type. We show here that, in fact, in a stable one-based theory, a similar type of construction can be done without the assumption of regularity. More precisely, we show that for any type q, the nontrivial part of q can be analyzed by generics of groups and that any nontrivial relation can be described by affine relations (Theorem A).This construction is then used to answer a question about homogeneity in pairs of models which is still open in the case of arbitrary stable theories (Theorem C).

scholarly journals COUNTABLE MODELS OF THE THEORIES OF BALDWIN–SHI HYPERGRAPHS AND THEIR REGULAR TYPES

2019 ◽  
Vol 84 (3) ◽  
pp. 1007-1019
Author(s):  
DANUL K. GUNATILLEKA
Keyword(s):  
Large Body ◽  
Countable Model ◽  
Stable Theory ◽  
Generic Structure ◽  
Elementary Chain ◽  
Regular Type ◽  
Image Position ◽  
Original Class ◽  
Countable Models

AbstractWe continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$ of countable models of the theory of a fixed Baldwin–Shi hypergraph with $\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $ if and only if the dimension of $\mathfrak{M}_\beta $ is at most the dimension of $\mathfrak{M}_\gamma $ and that each countable model is isomorphic to some $\mathfrak{M}_\beta $. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω-stable theory with a nonlocally modular regular type, answering a question of Pillay in [11].

A free pseudospace

2000 ◽  
Vol 65 (1) ◽  
pp. 443-460 ◽  
Author(s):  
Andreas Baudisch ◽  
Anand Pillay
Keyword(s):  
Stable Theory ◽  
Infinite Field ◽  
Morley Rank ◽  
Minimal Set ◽  
3 Dimensional ◽  
Regular Type ◽  
Finite Morley Rank ◽  
Dimensional Version ◽  
Stable Field

In this paper we construct a non-CM -trivial stable theory in which no infinite field is interpretable. In fact our theory will also be trivial and ω-stable, but of infinite Morley rank. A long term aim would be to find a non CM-trivial theory which has finite Morley rank (or is even strongly minimal) and does not interpret a field. The construction in this paper is direct, and is a “3-dimensional” version of the free pseudoplane. In a sense we are cheating: the original point of the notion of CM-triviality was to describe the geometry of a strongly minimal set, or even of a regular type. In our example, non-CM-triviality will come from the behaviour of three orthogonal regular types.A stable theory is said to be CM-trivial if whenever A ⊆ B and acl(Ac) ∩ acl(B) = acl(A) in Teq, then Cb(stp(c/A)) ⊆ Cb(stp(c/B)). ( An infinite stable field will not be CM-trivial.) The notion is due to Hrushovski [3], where he gave several equivalent definitions, as well as showing that his new strongly minimal sets constructed “ab ovo” were CM-trivial. The notion was studied further in [6] where it was shown that CM-trivial groups of finite Morley rank are nilpotent-by-finite. These results were generalized in various ways to the superstable case in [8].

A note on CM-triviality and the geometry of forking

2000 ◽  
Vol 65 (1) ◽  
pp. 474-480 ◽  
Author(s):  
Anand Pillay
Keyword(s):  
Finite Rank ◽  
Algebraic Closure ◽  
Simple Groups ◽  
General Context ◽  
Stable Theory ◽  
Geometric Properties ◽  
Regular Type ◽  
Superstable Theory ◽  
Minimal Sets ◽  
The Right

CM-triviality of a stable theory is a notion introduced by Hrushovski [1]. The importance of this property is first that it holds of Hrushovski's new non 1-based strongly minimal sets, and second that it is still quite a restrictive property, and forbids the existence of definable fields or simple groups (see [2]). In [5], Frank Wagner posed some questions about CM-triviality, asking in particular whether a structure of finite rank, which is “coordinatized” by CM-trivial types of rank 1, is itself CM-trivial. (Actually Wagner worked in a slightly more general context, adapting the definitions to a certain “local” framework, in which algebraic closure is replaced by P-closure, for P some family of types. We will, however, remain in the standard context, and will just remark here that it is routine to translate our results into Wagner's framework, as well as to generalise to the superstable theory/regular type context.) In any case we answer Wagner's question positively. Also in an attempt to put forward some concrete conjectures about the possible geometries of strongly minimal sets (or stable theories) we tentatively suggest a hierarchy of geometric properties of forking, the first two levels of which correspond to 1-basedness and CM-triviality respectively. We do not know whether this is a strict hierarchy (or even whether these are the “right” notions), but we conjecture that it is, and moreover that a counterexample to Cherlin's conjecture can be found at level three in the hierarchy.

scholarly journals The Urban River Syndrome: Achieving Sustainability Against a Backdrop of Accelerating Change

2021 ◽  
Vol 18 (12) ◽  
pp. 6406
Author(s):  
Martin Richardson ◽  
Mikhail Soloviev
Keyword(s):  
River Restoration ◽  
Native Species ◽  
Systems Approach ◽  
Similar Type ◽  
Urban River ◽  
Urban Rivers ◽  
River Ecology ◽  
Spatial And Temporal Scales ◽  
Natural Systems ◽  
Urban River Restoration

Human activities have been affecting rivers and other natural systems for millennia. Anthropogenic changes to rivers over the last few centuries led to the accelerating state of decline of coastal and estuarine regions globally. Urban rivers are parts of larger catchment ecosystems, which in turn form parts of wider nested, interconnected systems. Accurate modelling of urban rivers may not be possible because of the complex multisystem interactions operating concurrently and over different spatial and temporal scales. This paper overviews urban river syndrome, the accelerating deterioration of urban river ecology, and outlines growing conservation challenges of river restoration projects. This paper also reviews the river Thames, which is a typical urban river that suffers from growing anthropogenic effects and thus represents all urban rivers of similar type. A particular emphasis is made on ecosystem adaptation, widespread extinctions and the proliferation of non-native species in the urban Thames. This research emphasizes the need for a holistic systems approach to urban river restoration.

scholarly journals Crystal mush dykes as conduits for mineralising fluids in the Yerington porphyry copper district, Nevada

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Lawrence C. Carter ◽  
Ben J. Williamson ◽  
Simon R. Tapster ◽  
Catia Costa ◽  
Geoffrey W. Grime ◽  
...  
Keyword(s):  
Low Temperature ◽  
Cross Section ◽  
Porphyry Copper ◽  
Similar Type ◽  
Interconnected Network ◽  
Crystal Mush ◽  
Porphyry Deposit ◽  
Hydrothermal Quartz ◽  
Miarolitic Cavities

AbstractPorphyry-type deposits are the world’s main source of copper and molybdenum and provide a large proportion of gold and other metals. However, the mechanism by which mineralising fluids are extracted from source magmas and transported upwards into the ore-forming environment is not clearly understood. Here we use field, micro-textural and geochemical techniques to investigate field relationships and samples from a circa 8 km deep cross-section through the archetypal Yerington porphyry district, Nevada. We identify an interconnected network of relatively low-temperature hydrothermal quartz that is connected to mineralised miarolitic cavities within aplite dykes. We propose that porphyry-deposit-forming fluids migrated from evolved, more water-rich internal regions of the underlying Luhr Hill granite via these aplite dykes which contained a permeable magmatic crystal mush of feldspar and quartz. The textures we describe provide petrographic evidence for the transport of fluids through crystal mush dykes. We suggest that this process should be considered in future models for the formation of porphyry- and similar-type deposits.

Determinacy of Banach games

1985 ◽  
Vol 50 (1) ◽  
pp. 110-122
Author(s):  
Howard Becker
Keyword(s):  
Winning Strategy ◽  
Similar Type ◽  
Infinite Games ◽  
Real Numbers ◽  
Positive Real ◽  
Infinite Game ◽  
First Time

For any A ⊂ R, the Banach game B(A) is the following infinite game on reals: Players I and II alternately play positive real numbers a1; a2, a3, a4,… such that for n > 1, an < an−1. Player I wins iff ai exists and is in A.This type of game was introduced by Banach in 1935 in the Scottish Book [15], Problem 43. The (rather vague) problem which Banach posed was to characterize those sets A for which I (II) has a winning strategy in B(A). (There are three parts to Problem 43. In the first, Mazur defined a game G**(A) for every set A ⊂ R and conjectured that II has a winning strategy in G**(A) iff A is meager and I has a winning strategy in G**(A) iff A is comeager in some neighborhood; this conjecture was proved by Banach. Presumably Banach had this result in mind when he asked the question about B(A), and hoped for a similar type of characterization.) Incidentally, Problem 43 of the Scottish Book appears to be the first time infinite games of any sort were studied by mathematicians.This paper will not provide the reader with any answer to Banach's question. I know of no nontrivial way to characterize when player I (or II) wins, and I suspect there is none. This paper is concerned with a different (also rather vague) question: For which sets A is the Banach game B(A) determined? To say that B(A) is determined means, of course, that one of the players has a winning strategy for B(A).

scholarly journals Multisensor Fault Identification Scheme Based on Decentralized Sliding Mode Observers Applied to Reconfigurable Manipulators

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Zhao ◽  
Yuanchun Li
Keyword(s):  
Sliding Mode ◽  
Sliding Mode Observer ◽  
Fault Identification ◽  
Stable Theory ◽  
Sensor Fault ◽  
Identification Scheme ◽  
Neural Network Controller ◽  
Network Controller ◽  
Sliding Mode Observers ◽  
Reconfigurable Manipulators

This paper concerns with a fault identification scheme in a class of nonlinear interconnected systems. The decentralized sliding mode observer is recruited for the investigation of position sensor fault or velocity sensor fault. First, a decentralized neural network controller is proposed for the system under fault-free state. The diffeomorphism theory is utilized to construct a nonlinear transformation for subsystem structure. A simple filter is implemented to convert the sensor fault into pseudo-actuator fault scenario. The decentralized sliding mode observer is then presented for multisensor fault identification of reconfigurable manipulators based on Lyapunov stable theory. Finally, two 2-DOF reconfigurable manipulators with different configurations are employed to verify the effectiveness of the proposed scheme in numerical simulation. The results demonstrate that one joint’s fault does not affect other joints and the sensor fault can be identified precisely by the proposed decentralized sliding mode observer.

Prevention of Unintentional Esophageal Intubation

PEDIATRICS ◽  
1972 ◽  
Vol 49 (2) ◽  
pp. 313-313
Author(s):  
W. L. Niccum
Keyword(s):  
Endotracheal Tube ◽  
Young Patients ◽  
Similar Type ◽  
Esophageal Intubation ◽  
Endotracheal Tubes

I read with interest the experience of Stool, Johnson, and Rosenfeld in unintentionally introducing an endotracheal tube into the esophagus.1 I would like to relate that 15 years or so ago we had a similar type of problem with one of my young patients. We have solved the problem of unintentional esophageal intubation in a different and it seems to me a more simple way. Each one of our Foregger endotracheal tubes has on its proximal end approximately 6 in. of #3 black silk looped through a perforation on the tube.

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