A theorem on hyperhypersimple sets

1963 ◽  
Vol 28 (4) ◽  
pp. 273-278 ◽  
Author(s):  
Donald A. Martin
Keyword(s):  
Main Concern ◽  
Natural Question ◽  
Easy Consequence ◽  
Recursively Enumerable ◽  
Simple Set

Let be the class of recursively enumerable (r.e.) sets with infinite complements. A set M ϵ is maximal if every superset of M which is in is only finitely different from M. In [1] Friedberg shows that maximal sets exist, and it is an easy consequence of this fact that every non-simple set in has a maximal superset. The natural question which arises is whether or not this is also true for every simple set (Ullian [2]). In the present paper this question is answered negatively. However, the main concern of this paper is with demonstrating, and developing a few consequences of, what might be called the “density” of hyperhypersimple sets.

Some properties of the syntactic p-recursion categories generated by consistent, recursively enumerable extensions of Peano arithmetic.

1991 ◽  
Vol 56 (2) ◽  
pp. 643-660 ◽  
Author(s):  
Robert A. Di Paola ◽  
Franco Montagna
Keyword(s):  
Peano Arithmetic ◽  
Incompleteness Theorem ◽  
Easy Consequence ◽  
Recursively Enumerable ◽  
Bona Fide ◽  
Precise Relationship

The dominical categories were introduced by Di Paola and Heller, as a first step toward a category-theoretic treatment of the generalized first Godel incompleteness theorem [1]. In his Ph.D. dissertation [7], Rosolini subsequently defined the closely related p-categories, which should prove pertinent to category-theoretic representations of incompleteness for intuitionistic systems. The precise relationship between these two concepts is as follows: every dominical category is a pointed p-category, but there are p-categories, indeed pointed p-isotypes (all pairs of objects being isomorphic) with a Turing morphism that are not dominical. The first of these assertions is an easy consequence of the fact that in a dominical category C by definition the near product functor when restricted to the subcategory Ct, of total morphisms of C (as “total” is defined in [1]) constitutes a bona fide product such that the derived associativity and commutativity isomorphisms are natural on C × C × C and C × C, respectively, as noted in [7]. As to the second, p-recursion categories (that is, pointed p-isotypes having a Turing morphism) that are not dominical were defined and studied by Montagna in [6], the syntactic p-categories ST and S′T associated with consistent, recursively enumerable extensions of Peano arithmetic, PA. These merit detailed investigation on several counts.

Lambda theories allowing terms with a finite number of fixed points

2015 ◽  
Vol 27 (3) ◽  
pp. 405-427
Author(s):  
BENEDETTO INTRIGILA ◽  
RICHARD STATMAN
Keyword(s):  
Finite Number ◽  
Fixed Points ◽  
Related Question ◽  
Natural Question ◽  
Open Problems ◽  
Complete Answer ◽  
Recursively Enumerable

A natural question in the λ-calculus asks what is the possible number of fixed points of a combinator (closed term). A complete answer to this question is still missing (Problem 25 of TLCA Open Problems List) and we investigate the related question about the number of fixed points of a combinator in λ-theories. We show the existence of a recursively enumerable lambda theory where the number is always one or infinite. We also show that there are λ-theories such that some terms have only two fixed points. In a first example, this is obtained by means of a non-constructive (more precisely non-r.e.) λ-theory where the range property is violated. A second, more complex example of a non-r.e. λ-theory (with a higher unsolvability degree) shows that some terms can have only two fixed points while the range property holds for every term.

Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion

1989 ◽  
Vol 54 (4) ◽  
pp. 1288-1323 ◽  
Author(s):  
C. G. Jockusch ◽  
M. Lerman ◽  
R. I. Soare ◽  
R. M. Solovay
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Equivalence Relations ◽  
Main Concern ◽  
Strict Sense ◽  
Recursively Enumerable ◽  
Completeness Criterion ◽  
Starting Point ◽  
Recursively Enumerable Sets ◽  
Point Form

Let We be the eth recursively enumerable (r.e.) set in a standard enumeration. The fixed point form of Kleene's recursion theorem asserts that for every recursive function f there exists e which is a fixed point of f in the sense that We = Wf(e). In this paper our main concern is to study the degrees of functions with no fixed points. We consider both fixed points in the strict sense above and fixed points modulo various equivalence relations on recursively enumerable sets.Our starting point for the investigation of the degrees of functions without (strict) fixed points is the following result due to M. M. Arslanov [A1, Theorem 1] and known as the Arslanov completeness criterion. Proofs of this result may also be found in [So1, Theorem 1.3] and [So2, Chapter 12], and we will give a game version of the proof in §5 of this paper.Theorem 1.1 (Arslanov). Let A be an r.e. set. Then A is complete (i.e. A has degree0′) iff there is a function f recursive in A with no fixed point.

scholarly journals An Extremal Graph Problem with a Transcendental Solution

2018 ◽  
Vol 28 (2) ◽  
pp. 303-324 ◽  
Author(s):  
DHRUV MUBAYI ◽  
CAROLINE TERRY
Keyword(s):  
Number Theory ◽  
Related Problem ◽  
Extremal Graph ◽  
Natural Question ◽  
Extremal Combinatorics ◽  
Easy Consequence ◽  
Vertex Set ◽  
Schanuel's Conjecture ◽  
Transcendental Solution ◽  
Shed Light

We prove that the number of multigraphs with vertex set {1, . . .,n} such that every four vertices span at most nine edges isan2+o(n2)whereais transcendental (assuming Schanuel's conjecture from number theory). This is an easy consequence of the solution to a related problem about maximizing the product of the edge multiplicities in certain multigraphs, and appears to be the first explicit (somewhat natural) question in extremal graph theory whose solution is transcendental. These results may shed light on a question of Razborov, who asked whether there are conjectures or theorems in extremal combinatorics which cannot be proved by a certain class of finite methods that include Cauchy–Schwarz arguments.Our proof involves a novel application of Zykov symmetrization applied to multigraphs, a rather technical progressive induction, and a straightforward use of hypergraph containers.

Recursively enumerable generic sets

1982 ◽  
Vol 47 (4) ◽  
pp. 809-823 ◽  
Author(s):  
Wolfgang Maass
Keyword(s):  
Essential Feature ◽  
Turing Degree ◽  
New Class ◽  
Recursively Enumerable ◽  
Simple Set ◽  
Recursively Enumerable Sets

AbstractWe show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0′. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice ℰ of recursively enumerable sets with inclusion. We introduce the notion of a promptly simple set. This describes the essential feature of r.e. generic sets with respect to automorphism constructions.

IMPLEMENTASI KINERJA KEUANGAN TERHADAP NILAI SPIRITUALITAS PRIBADI

2012 ◽  
Vol 16 (3) ◽  
pp. 332
Author(s):  
Whedy Prasetyo
Keyword(s):  
Corporate Governance ◽  
Corporate Social Responsibility ◽  
Social Responsibility ◽  
Financial Performance ◽  
Annual Report ◽  
Main Concern ◽  
Good Corporate Governance ◽  
Corporate Social ◽  
The Relationship ◽  
Personal Spirituality

Development of financial performance in the application of Good Corporate Governance and Corporate Social Responsibility which affects the values of honesty private individuals, in order to be able to run the accountability, value for money, fairness in financial management, transparency, control, and free of conflicts of interest (independence). The main concern in this study is focused on achieving value personal spirituality through the financial performance and capabilities of Good Corporate Governance (GCG) and Corporate Social Responsibility (CSR) in moderating the relationship with the financial performance of value personal spirituality. This study is a descriptive verifikatif. The unit of analysis in this study was 15 companies in Indonesia with a policy that has been applied through the concept since January of 2008 until now, with the support of the annual report of the company, the company's financial statements, company reports to the disclosure of Good Corporate Governance and Corporate Social Responsibility in the annual report. Overall reports published successively during the years 2008-2011. The results of this study indicate financial performance affects the value of personal spirituality, and for variable GCG obtained results that could moderate the relationship of financial performance to the value of personal spirituality. But for the disclosure of CSR variables obtained results can’t moderate the relationship with the financial performance of personal spirituality.

Differences between Feminist and Mainstream Approaches to Social Science, Most Notably in Sociology, Political Science, Anthropology and History

2014 ◽  
Vol 2 (1) ◽  
pp. 47-50
Author(s):  
Senka Ena Majetic
Keyword(s):  
Social Science ◽  
Political Science ◽  
Main Concern ◽  
Feminist Methodology ◽  
Feminist Writing

Abstract - It is widely accepted among feminists that feminism implies a distinctive approach to inquiry. And for some this is not just a matter of the grounds on which topics are selected for investigation, or even of the theoretical ideas that are treated as relevant. Rather, feminism is taken to carry distinctive methodological and epistemological implications (Hammersley, 1995: 45). In this paper I want to assess the arguments for a distinctively feminist methodology. My first task, though, is to provide some detail about what this is taken to entail. There are, of course, important differences among feminists who have written on this topic, and in the course of the discussion I will highlight some of these. I certainly do not want to suggest that what I am assessing is a single position, nor am I claiming to represent the basis on which most feminists actually do research. My main concern here is solely with feminist writing about methodology.

Analyzing the development of approaches to company performance measurement

2020 ◽  
Vol 19 (6) ◽  
pp. 1173-1188
Author(s):  
A.B. Kogan ◽  
A.N. Pristavka
Keyword(s):  
Comparative Analysis ◽  
Performance Measurement ◽  
Business Environment ◽  
Theoretical Research ◽  
Effectiveness Evaluation ◽  
Economic Science ◽  
Company Performance ◽  
Financial Indicators ◽  
Methodological Framework ◽  
Simple Set

Subject. The article presents various definitions of the efficiency concept, their changes as the economic science evolves, and describes various methods to measure company performance efficiency, ranging from a simple set of financial indicators to comprehensive systems for effectiveness evaluation. Objectives. The purpose of the study is to systematize the said definitions and identify a category that will meet the current condition of business environment. Methods. The study rests on the retrospective and comparative analysis of interpretations of the efficiency concept in the economic science. We also employ the historical and logical methods of general theoretical research. Results. We identify three approaches to the interpretation of the efficiency concept. Within the selected approaches, we consider the main methods for company performance measurement that have emerged since 1914. The paper formulates criteria, which were used to carry out the comparative analysis of these methods. The analysis enabled to trace all changes in the methods. Conclusions. We propose to use the term Integrated Company Efficiency and to develop methodological framework for measuring the comprehensive efficiency of companies operating in various industries.

Noordin Sopite, Chew Lay See and Lim Siang Jin (eds.). ASI:.""AN at the OOSSToads: Obstacles, Options and Opportunities in Economic Cooperatjon. Malaysia: Institute of Strategic and International Studies (ISIS) 1987.577 pp.Price: (hardbound edition) USS 25.

1988 ◽  
Vol 27 (2) ◽  
pp. 219-222
Author(s):  
Khwaja Sarmad
Keyword(s):  
Economies Of Scale ◽  
Joint Venture ◽  
Main Concern ◽  
International Studies ◽  
Industrialized Countries ◽  
Preferential Trade ◽  
Governmental Organization ◽  
Asean Member ◽  
Long Time ◽  
Preferential Trading Arrangements

The Association of Southeast Asian Nations (ASEAN) was established In 1967 as a loosely structured inter-governmental organization, which provided a framework for discussing problems that required a regional solution. For a long time, the reduction of regional political tensions remained the main concern of ASEAN. Serious efforts towards promoting intra-regional co-operation began in 1976 with emphasis on trade liberalization and industrial co-operation. But apart from a few cases, involving the regional economies and collective external bargaining, the record of economic co-operation has been poor, because of different levels of economic development of the member countries, mutually competitive exports.. inward• looking industrial policies and heavy dependence on the industrialized countries for investment, technology and trade. So far, there have been only three intra-ASEAN agreements to promote market sharing and a pooling of resources: the preferential trade arrangements, the industrial complementation agreement, designed to develop links in certain industries to achieve greater economies of scale, and the industrial joint venture agreement, which provides preferential treatment for products of joint ventures involving the companies of at least two ASEAN member countries. However the joint venture scheme has had only limited success because of delays in implementation, while the scope of the preferential trading arrangements has been limited by the consensus approach in solving outstanding issues and by the concern of higher-tariff member countries to protect domestic production and employment. As a result, tariffs have been reduced only on intra-regional trade of selected non-sensitive items. Most of the items covered in the preferential trade agreements have low trade content and minimal trade potential. The arrangements have also been difficult to manage because of problems of administering the rules of origin.

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