scholarly journals BINARY PRIMITIVE HOMOGENEOUS SIMPLE STRUCTURES

2017 ◽  
Vol 82 (1) ◽  
pp. 183-207 ◽  
Author(s):  
VERA KOPONEN
Keyword(s):  
Algebraic Closure ◽  
The Other ◽  
Equivalence Relations ◽  
Complete Theory ◽  
Future Research ◽  
Random Structure ◽  
Homogeneous Structures ◽  
Image Position

AbstractSuppose that ${\cal M}$ is countable, binary, primitive, homogeneous, and simple. We prove that the SU-rank of the complete theory of ${\cal M}$ is 1 and hence 1-based. It follows that ${\cal M}$ is a random structure. The conclusion that ${\cal M}$ is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that the generic tetrahedron-free 3-hypergraph is 1-based requires some work (it is known that it has the other properties) since this notion is defined in terms of imaginary elements. This is partly why we also characterize equivalence relations which are definable without parameters in the context of ω-categorical structures with degenerate algebraic closure. Another reason is that such characterizations may be useful in future research about simple (nonbinary) homogeneous structures.

scholarly journals ON CONSTRAINTS AND DIVIDING IN TERNARY HOMOGENEOUS STRUCTURES

2018 ◽  
Vol 83 (04) ◽  
pp. 1691-1721 ◽  
Author(s):  
VERA KOPONEN
Keyword(s):  
Algebraic Closure ◽  
Equivalence Relations ◽  
Finite Sets ◽  
Uncountable Family ◽  
Homogeneous Structures ◽  
Image Position

AbstractLet ${\cal M}$ be ternary, homogeneous and simple. We prove that if ${\cal M}$ is finitely constrained, then it is supersimple with finite SU-rank and dependence is k-trivial for some k < ω and for finite sets of real elements. Now suppose that, in addition, ${\cal M}$ is supersimple with SU-rank 1. If ${\cal M}$ is finitely constrained then algebraic closure in ${\cal M}$ is trivial. We also find connections between the nature of the constraints of ${\cal M}$, the nature of the amalgamations allowed by the age of ${\cal M}$, and the nature of definable equivalence relations. A key method of proof is to “extract” constraints (of ${\cal M}$) from instances of dividing and from definable equivalence relations. Finally, we give new examples, including an uncountable family, of ternary homogeneous supersimple structures of SU-rank 1.

ON ISOMORPHISM CLASSES OF COMPUTABLY ENUMERABLE EQUIVALENCE RELATIONS

2019 ◽  
Vol 85 (1) ◽  
pp. 61-86 ◽  
Author(s):  
URI ANDREWS ◽  
SERIKZHAN A. BADAEV
Keyword(s):  
Explicit Construction ◽  
The Other ◽  
Equivalence Relations ◽  
Index Set ◽  
Isomorphism Classes ◽  
Closed Sets ◽  
Open Questions ◽  
Index Sets ◽  
Image Position ◽  
Computably Enumerable

AbstractWe examine how degrees of computably enumerable equivalence relations (ceers) under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete ceers contained in the degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots ,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left( {{E_i}} \right)$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers.

On the category of models of a complete theory

1982 ◽  
Vol 47 (2) ◽  
pp. 249-266 ◽  
Author(s):  
Daniel Lascar
Keyword(s):  
The Other ◽  
Complete Theory ◽  
Semi Group ◽  
Group Of Automorphisms ◽  
Infinite Sets ◽  
Image Position ◽  
The Given

Let T be a countable complete theory and C(T) the category whose objects are the models of T and morphisms are the elementary maps. The main object of this paper will be the study of C(T). The idea that a better understanding of the category may give us model theoretic information about T is quite natural: The (semi) group of automorphisms (endomorphisms) of a given structure is often a powerful tool for studying this structure. But certainly, one of the very first questions to be answered is: “to what extent does this category C(T) determine T?”There is some obvious limitation: for example let T0 be the theory of infinite sets (in a language containing only =) and T1 the theory, in the language ( =, U(ν0),f(ν0)) stating that:(1) U is infinite.(2)f is a bijective map from U onto its complement.It is quite easy to see that C(T0) is equivalent to C(T1). But, in this case, T0 and T1 can be “interpreted” each in the other. To make this notion of interpretation precise, we shall associate with each theory T a category, loosely denoted by T, defined as follows:(1) The objects are the formulas in the given language.(2) The morphisms from into are the formulas such that(i.e. f defines a map from ϕ into ϕ; two morphisms defining the same map in all models of T should be identified).

Children With Intellectual Disability and Victimization: A Logistic Regression Analysis

2021 ◽  
pp. 107755952199417
Author(s):  
Katherine R. Brendli ◽  
Michael D. Broda ◽  
Ruth Brown
Keyword(s):  
Logistic Regression ◽  
Regression Analysis ◽  
Intellectual Disability ◽  
Logistic Regression Analysis ◽  
District Of Columbia ◽  
The Other ◽  
Future Research ◽  
Common Assumption ◽  
Research And Practice ◽  
Demographic Correlates

It is a common assumption that children with disabilities are more likely to experience victimization than their peers without disabilities. However, there is a paucity of robust research supporting this assumption in the current literature. In response to this need, we conducted a logistic regression analysis using a national dataset of responses from 26,572 parents/caregivers to children with and without disabilities across all 50 states, plus the District of Columbia. The purpose of our study was to acquire a greater understanding of the odds of victimization among children with and without intellectual disability (ID), while controlling for several child and parent/adult demographic correlates. Most notably, our study revealed that children with ID have 2.84 times greater odds of experiencing victimization than children without disabilities, after adjusting for the other predictors in the model. Implications for future research and practice are discussed.

scholarly journals A taxonomy of antonymy in Arabic: Egyptian and Saudi proverbs in comparison

2021 ◽  
Vol 7 (1) ◽  
pp. 200-222
Author(s):  
Hamada Hassanein ◽  
Mohammad Mahzari
Keyword(s):  
Main Clause ◽  
The Other ◽  
Subordinate Clause ◽  
Future Research ◽  
Case Marking ◽  
News Discourse ◽  
Discourse Functions ◽  
Syntactic Frames

Abstract This study has set out to identify, quantify, typify, and exemplify the discourse functions of canonical antonymy in Arabic paremiography by comparing two manually collected datasets from Egyptian and Saudi (Najdi) dialects. Building upon Jones’s (2002) most extensive and often-cited classification of the discourse functions of antonyms as they co-occur within syntactic frames in news discourse, the study has substantially revised this classification and developed a provisional and dynamic typology thereof. Two major textual functions are found to be quantitatively significant and qualitatively preponderant: ancillarity (wherein an A-pair of canonical antonyms project their antonymicity onto a more important B-pair) and coordination (wherein one antonym holds an inclusive or exhaustive relation to another antonym). Three new functions have been developed and added to the retrieved classification: subordination (wherein one antonym occurs in a subordinate clause while the other occurs in a main clause), case-marking (wherein two opposite cases are served by two antonyms), and replacement (wherein one antonym is substituted with another). Semicanonical and noncanonical guises of antonymy are left and recommended for future research.

scholarly journals The Dissociation of the Compound of Iodine and Thio-urea

1904 ◽  
Vol 24 ◽  
pp. 233-239 ◽  
Author(s):  
Hugh Marshall
Keyword(s):  
Nitric Acid ◽  
General Formula ◽  
Free Acid ◽  
The Other ◽  
Image Position

When thio-urea is treated with suitable oxidising agents in presence of acids, salts are formed corresponding to the general formula (CSN2H4)2X2:—Of these salts the di-nitrate is very sparingly soluble, and is precipitated on the addition of nitric acid or a nitrate to solutions of the other salts. The salts, as a class, are not very stable, and their solutions decompose, especially on warming, with formation of sulphur, thio-urea, cyanamide, and free acid. A corresponding decomposition results immediately on the addition of alkali, and this constitutes a very characteristic reaction for these salts.

Dirty Work and Dirtier Work: Differences in Countering Physical, Social, and Moral Stigma

2014 ◽  
Vol 10 (1) ◽  
pp. 81-108 ◽  
Author(s):  
Blake E. Ashforth ◽  
Glen E. Kreiner
Keyword(s):  
Distinct Group ◽  
The Other ◽  
Future Research ◽  
Identity Threat ◽  
Dirty Work ◽  
Exotic Dancers ◽  
Organization Level ◽  
Group A

The literature on dirty work has focused on what physically (e.g., garbage collectors), socially (e.g., addiction counsellors), and morally (e.g., exotic dancers) stigmatized occupations have in common, implying that dirty work is a relatively monolithic construct. In this article, we focus on thedifferencesbetween these three forms of dirty work and how occupational members collectively attempt to counter the particular stigma associated with each. We argue that the largest differences are between moral dirty work and the other two forms; if physical and social dirty work tend to be seen as more necessary than evil, then moral dirty work tends to be seen as more evil than necessary. Moral dirty work typically constitutes a graver identity threat to occupational members, fostering greater entitativity (a sense of being a distinct group), a greater reliance on members as social buffers, and a greater use of condemning condemners and organization-level defensive tactics. We develop a series of propositions to formalize our arguments and suggest how this more nuanced approach to studying dirty work can stimulate and inform future research.

Extremely undecidable sentences

1982 ◽  
Vol 47 (1) ◽  
pp. 191-196 ◽  
Author(s):  
George Boolos
Keyword(s):  
Modal Logic ◽  
The Other ◽  
Propositional Modal Logic ◽  
Image Position

Let ‘ϕ’, ‘χ’, and ‘ψ’ be variables ranging over functions from the sentence letters P0, P1, … Pn, … of (propositional) modal logic to sentences of P(eano) Arithmetic), and for each sentence A of modal logic, inductively define Aϕ by[and similarly for other nonmodal propositional connectives]; andwhere Bew(x) is the standard provability predicate for PA and ⌈F⌉ is the PA numeral for the Gödel number of the formula F of PA. Then for any ϕ, (−□⊥)ϕ = −Bew(⌈⊥⌉), which is the consistency assertion for PA; a sentence S is undecidable in PA iff both and , where ϕ(p0) = S. If ψ(p0) is the undecidable sentence constructed by Gödel, then ⊬PA (−□⊥→ −□p0 & − □ − p0)ψ and ⊢PA(P0 ↔ −□⊥)ψ. However, if ψ(p0) is the undecidable sentence constructed by Rosser, then the situation is the other way around: ⊬PA(P0 ↔ −□⊥)ψ and ⊢PA (−□⊥→ −□−p0 & −□−p0)ψ. We call a sentence S of PA extremely undecidable if for all modal sentences A containing no sentence letter other than p0, if for some ψ, ⊬PAAψ, then ⊬PAAϕ, where ϕ(p0) = S. (So, roughly speaking, a sentence is extremely undecidable if it can be proved to have only those modal-logically characterizable properties that every sentence can be proved to have.) Thus extremely undecidable sentences are undecidable, but neither the Godel nor the Rosser sentence is extremely undecidable. It will follow at once from the main theorem of this paper that there are infinitely many inequivalent extremely undecidable sentences.

On functional Nörlund methods

1970 ◽  
Vol 67 (1) ◽  
pp. 47-60 ◽  
Author(s):  
B. Choudhary
Keyword(s):  
The Other ◽  
Integral Transformations ◽  
Other Hand ◽  
Nörlund Means ◽  
The One ◽  
Image Position

Integral transformations analogous to the Nörlund means have been introduced and investigated by Kuttner, Knopp and Vanderburg(6), (5), (4). It is known that with any regular Nörlund mean (N, p) there is associated a functionregular for |z| < 1, and if we have two Nörlund means (N, p) and (N, r), where (N, pr is regular, while the function is regular for |z| ≤ 1 and different) from zero at z = 1, then q(z) = r(z)p(z) belongs to a regular Nörlund mean (N, q). Concerning Nörlund means Peyerimhoff(7) and Miesner (3) have recently obtained the relation between the convergence fields of the Nörlund means (N, p) and (N, r) on the one hand and the convergence field of the Nörlund mean (N, q) on the other hand.

scholarly journals Distribution of rational points on the real line

1973 ◽  
Vol 15 (2) ◽  
pp. 243-256 ◽  
Author(s):  
T. K. Sheng
Keyword(s):  
Algebraic Number ◽  
Rational Number ◽  
Real Line ◽  
Rational Points ◽  
The Other ◽  
Liouville Numbers ◽  
The Real ◽  
Other Hand ◽  
Image Position

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.

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