A Borel reductibility theory for classes of countable structures

1989 ◽  
Vol 54 (3) ◽  
pp. 894-914 ◽  
Author(s):  
Harvey Friedman ◽  
Lee Stanley
Keyword(s):  
Point Of View ◽  
Algebraic Structures ◽  
Main Thrust ◽  
Similarity Type ◽  
Borel Class ◽  
Natural Classes

AbstractWe introduce a reducibility preordering between classes of countable structures, each class containing only structures of a given similarity type (which is allowed to vary from class to class). Though we sometimes work in a slightly larger context, we are principally concerned with the case where each class is an invariant Borel class (i.e. the class of all models, with underlying set = ω, of an Lω1ω sentence; from this point of view, the reducibility can be thought of as a (rather weak) sort of Lω1ω-interpretability notion). We prove a number of general results about this notion, but our main thrust is to situate various mathematically natural classes with respect to the preordering, most notably classes of algebraic structures such as groups and fields.

scholarly journals COMPUTATIONAL COMPLEXITY OF TERM-EQUIVALENCE

1999 ◽  
Vol 09 (01) ◽  
pp. 113-128 ◽  
Author(s):  
CLIFFORD BERGMAN ◽  
DAVID JUEDES ◽  
GIORA SLUTZKI
Keyword(s):  
Computational Complexity ◽  
Algebraic Structures ◽  
Exponential Time ◽  
Similarity Type ◽  
Finite Algebras ◽  
Term Equivalence

Two algebraic structures with the same universe are called term-equivalent if they have the same clone of term operations. We show that the problem of determining whether two finite algebras of finite similarity type are term-equivalent is complete for deterministic exponential time.

scholarly journals Rule of law as a national phenomenon people's consciousness

2019 ◽  
pp. 58-67
Author(s):  
Olena Panchenko
Keyword(s):  
Rule Of Law ◽  
Legal Culture ◽  
Point Of View ◽  
Legal Consciousness ◽  
Personality Structure ◽  
Natural Basis ◽  
Main Thrust ◽  
The Rule Of Law ◽  
The People ◽  
The Right

The article is devoted to the study of the rule of law as a social phenomenon, which is formed and viewed by us through the national legal consciousness of the people. These philosophical and legal categories are important for the formation of the correct (tested by time and reality) and the right awareness of society of their behavior, as well as effectively serve from the point of view of natural and legal influence on the formation and implementation of legal relations, and are a natural basis of law itself The main thrust of this article is that the rule of law in society depends to some extent on the national spirit of law and finds its foundations in the mentality of the people themselves. Historically, state and natural features of the rule of law further influence the formation of legal consciousness and legal culture in particular. Willingness is an important element of the national phenomenon in the consciousness of our people. The rule of law is the legal culture and legal consciousness that are closely linked to the national elements and characteristics of the people themselves who use the phenomenon. Since the rule of law is largely inherently in the form of ideas and perceptions, it is appropriate to note that such perceptions are necessarily nationalist in nature. Legal ideas and national ideas are fundamental to the formation and awareness of the rule of law Just as the rule of law is directly related to human nature, its national identity, and its vitality, it directly controls the sphere of human behavior and actions. The basic tenets that are enshrined in the rule of law are the ideas of freedom and justice. The rule of law as a national phenomenon of justice of the people is of the highest philosophical and legal value, since its place in the legal reality is determined by social and national factors and personality structure. Keywords: law, rule of law, phenomenon, national, legal consciousness.

scholarly journals Fuzzy -Continuous Posets

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
S. P. Rao ◽  
Q. G. Li
Keyword(s):  
Extension Theorem ◽  
Algebraic Structures ◽  
Fuzzy Subset ◽  
Closure Operators ◽  
Continuous Map ◽  
Monotone Map ◽  
Continuous Maps ◽  
Continuous Closure ◽  
Natural Classes

The aim of this paper is to generalize fuzzy continuous posets. The concept of fuzzy subset system on fuzzy posets is introduced; some elementary definitions such as fuzzy -continuous posets and fuzzy -algebraic posets are given. Furthermore, we try to find some natural classes of fuzzy -continuous maps under which the images of such fuzzy algebraic structures can be preserved; we also think about fuzzy -continuous closure operators in alternative ways. An extension theorem is presented for extending a fuzzy monotone map defined on the -compact elements to a fuzzy -continuous map defined on the whole set.

scholarly journals Literature Survey on Non-Associative Rings and Developments

2019 ◽  
Vol 12 (2) ◽  
pp. 370-408 ◽  
Author(s):  
Syed Tariq Shah ◽  
Asima Razzaque ◽  
Inayatur Rehman ◽  
Muhammad Asif Gondal ◽  
Muhammad Iftikhar Faraz ◽  
...  
Keyword(s):  
Literature Survey ◽  
Point Of View ◽  
Theoretical Point ◽  
Algebraic Structures ◽  
Comprehensive Survey ◽  
Associative Rings

In this paper we present a comprehensive survey and developments of existing literature of non-associative rings and enumerate some of their various applications in different directions to date. These applications explain the voluminous work in different fields of non-associative rings and through which various algebraic structures in theoretical point of view could be developed.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

How a sheperd guides a sheep herd?

1984 ◽  
Vol 75 ◽  
pp. 331-337
Author(s):  
Richard Greenberg
Keyword(s):  
Point Of View ◽  
Single Ring ◽  
Damping Effects ◽  
Ring Particle

ABSTRACTThe mechanism by which a shepherd satellite exerts a confining torque on a ring is considered from the point of view of a single ring particle. It is still not clear how one might most meaningfully include damping effects and other collisional processes into this type of approach to the problem.

The growth of mica polytypes as studied by conventional and high-resolution TEM

1983 ◽  
Vol 41 ◽  
pp. 174-177
Author(s):  
A. Baronnet ◽  
M. Amouric
Keyword(s):  
Water Pressure ◽  
Point Of View ◽  
Temperature Fields ◽  
Natural Occurrence ◽  
Growth Mechanisms ◽  
Long Period ◽  
High Resolution Tem ◽  
Layer Stacking ◽  
Experimental Works ◽  
Potential Use

The origin of mica polytypes has long been a challenging problem for crystal- lographers, mineralogists and petrologists. From the petrological point of view, interest in this field arose from the potential use of layer stacking data to furnish further informations about equilibrium and/or kinetic conditions prevailing during the crystallization of the widespread mica-bearing rocks. From the compilation of previous experimental works dealing with the occurrence domains of the various mica "polymorphs" (1Mr, 1M, 2M1, 2M2 and 3T) within water-pressure vs temperature fields, it became clear that most of these modifications should be considered as metastable for a fixed mica species. Furthermore, the natural occurrence of long-period (or complex) polytypes could not be accounted for by phase considerations. This highlighted the need of a more detailed kinetic approach of the problem and, in particular, of the role growth mechanisms of basal faces could play in this crystallographic phenomenon.

Radiation Damage in Ceramics

1982 ◽  
Vol 40 ◽  
pp. 600-603
Author(s):  
T. E. Mitchell ◽  
M. R. Pascucci ◽  
R. A. Youngman
Keyword(s):  
Radiation Damage ◽  
Outer Space ◽  
Point Of View ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Storage Media ◽  
Transmission Electron ◽  
Fundamental Point ◽  
Small Defect ◽  
Present Understanding

1. Introduction. Studies of radiation damage in ceramics are of interest not only from a fundamental point of view but also because it is important to understand the behavior of ceramics in various practical radiation enyironments- fission and fusion reactors, nuclear waste storage media, ion-implantation devices, outer space, etc. A great deal of work has been done on the spectroscopy of point defects and small defect clusters in ceramics, but relatively little has been performed on defect agglomeration using transmission electron microscopy (TEM) in the same kind of detail that has been so successful in metals. This article will assess our present understanding of radiation damage in ceramics with illustrations using results obtained from the authors' work.

Structural aspects of osmoregulation in porphyra

1978 ◽  
Vol 36 (2) ◽  
pp. 412-413
Author(s):  
C. Wiencke ◽  
A. Lauchli
Keyword(s):  
Culture Medium ◽  
Point Of View ◽  
Chemical Fixation ◽  
Cellular Organization ◽  
Osmotic Adaptation ◽  
Osmotic Balance ◽  
Activity Of Enzymes ◽  
Osmotic Agents ◽  
Vacuolar System ◽  
Structural Aspects

Osmoregulatory mechanisms in algae were investigated mainly from a physiological point of view (KAUSS 1977, HELLEBUST 1976). In Porphyra two osmotic agents, i. e. floridoside/isofloridoside (KAUSS 1968) and certain ions, such as K+ and Na+(EPPLEY et al. 1960) are considered for osmotic balance. Accumulations of ions (particularly Na+) in the cytoplasm during osmotic adaptation is improbable, because the activity of enzymes is generally inhibited by high ionic concentrations (FLOWERS et al. 1977).The cellular organization of Porphyra was studied with special emphasis on the development of the vacuolar system under different hyperosmotic conditions. Porphyra was cultivated at various strengths of the culture medium ASP 12 (PROVASOLI 1961) ranging from normal to 6 times concentrated (6x) culture medium. Por electron microscopy freeze fracturing was used (specimens fixed in 2% glutaraldehyde and incubated in 30% glycerol, preparation in a BALZERS BA 360 M apparatus), because chemical fixation gave poor results.

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