Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations

There is a fascinating interplay and overlap between recursion theory and descriptive set theory. A particularly beautiful source of such interaction has been Martin's conjecture on Turing invariant functions. This longstanding open problem in recursion theory has connected to many problems in descriptive set theory, particularly in the theory of countable Borel equivalence relations. In this paper, we shall give an overview of some work that has been done on Martin's conjecture, and applications that it has had in descriptive set theory. We will present a long unpublished result of Slaman and Steel that arithmetic equivalence is a universal countable Borel equivalence relation. This theorem has interesting corollaries for the theory of universal countable Borel equivalence relations in general. We end with some open problems, and directions for future research.Comment: Corrected typo

Demographics and the Political Sustainability of Pay-as-you-go Social Security

The net present value of costs and benefits from a pay-as-you-go social security system are negative for young people and positive for the elderly. If people all vote their financial self-interest, there will be a pivotal age such that those who are younger favor smaller social security benefits and those who are older will favor larger benefits. For persons of each age and sex, we estimate the expected present value gained or lost from a small permanent increase in the amount of benefits, where the cost of these benefits is divided equally among the population of working age. Assuming that everyone votes his or her long run financial self-interest, and calculating the number of voters in the population of each age and sex, we can determine whether there is majority support for an increase or a decrease in social security benefits. We use statistics on the age distribution and mortality rates for the United States to explore the sensitivity of political support for social security to alternative assumptions about the discount rate, excess burden in taxation, voter participation rates, and birth, death, and migration rates. We find that a once-and-for-all decrease in benefits would be defeated by a majority of selfish voters under a wide range of parameters. We also study the predicted majority outcomes of votes on changing the retirement age.

The Lack Of Industrialization, The Limited Number Of Private Corporations, And The Retardation Of Management In Private Business Enterprises In Greece

The purpose of this article was to examine and evaluate how 1) the late arrival of industrialization in Greece and the subsequent de-industrialization of the country deterred the formation and expansion of private corporations and impeded the mergers of small private enterprises in creating larger ones in the corporate form of business and 2) how the limited presence of private corporations retarded the development of management. Corporations are created through a planned initial formation and/or through the mergers of smaller corporate and non-corporate entities, such as proprietorships, partnerships, and family-owned non-stock corporations. Subsequently, the ample factors of production within the corporation allow the formation of professional management and the principles of organization which result in advanced managerial and organizational performance

Mergers Of Private Enterprises: A Powerful Force For The Development Of Private Business Organizations In Latin America - The Case Of Ecuador

The purpose of this article was to assess the scale of mergers of small and medium-size private business organizations in Ecuador over the past ten years and to determine if the ownership and management of such enterprises have the desire in merging with other Ecuadorian business organizations. Such mergers create larger business enterprises that allow the appearance, sustenance, and development of the principles of organization and precipitate the need for commensurate managerial education for their management and ownership. It was determined, in this study, that only a very limited number of mergers have taken place during the past ten years  and that the entrepreneurial mindset of business owners and their managers is not favoring mergers. The ownership and management of small and medium-size Ecuadorian business organizations do not understand the benefits derived from mergers. The study noted that Ecuador’s business owners and their managers are traditionally accustomed to operating with obsolete management methods and controls that suppress opportunities leading to organizational development

The Necessity Of Strategic Leadership In Corporate Sustainability

The purpose of this article is to present the necessity of having strategic leadership in business corporations that practice corporate sustainability. There are three areas that corporate sustainability focuses upon: Ecological, sociological, and corporate/business. Corporate sustainability requires strategic leadership in order to interact with these three dynamic and divergent areas. Strategic leaders communicate their vision to their managers and employees and remain in continuous and uninterrupted contact with the former who are dexterously empowered by their leaders to assume supportive roles for the communication of their leaders strategic vision to internal and external stakeholders of the organization. Strategic thinking is utilized by strategic leaders and has to do with the analysis and evaluation of the existing internal and external environments of the organization and that of how changes in both environments can affect the organization. Strategic leaders utilize strategic intent that includes focusing the organizations intention to operate strategically. Flexibility is the ability of strategic leaders to analyze, evaluate, and respond to changes in both the internal and external environment of their organizations. Strategic leaders initiate changes because of the demands that emanate from the external and the internal environments of the organization. Strategic leadership changes are dramatic ones and their implementation requires the integration of vision, flexibility, and the support of the managers of the organization

The Importance Of Imbedding The Concept Of Continuous Development In The Formulation Of Global Strategies

This article deals with the importance of incorporating the concept of continuous development in the formulation of strategy in global organizations where the strategists have to focus their attention on both the external and internal environmental forces of the firms. In the external environment, the social and task elements are to be analyzed and examined; the latter include the industry analysis. In the internal environment, analysis and evaluation must take place in the organizational structure, principles of organization, culture, and the human element.  Continuous development is within the concept of organizational development, which is a planned change effort that involves all the parts of the organization. It is initiated and managed from the top hierarchy of the system and is designed to increase organizational effectiveness. Continuous development must concentrate on the development of the organizational structure, policies and procedures, performance appraisals, the management, the employees, communications, and on the leadership of the organization because these elements are fundamental in the corporate strategy. The continuous developmental process is concentrated within the internal environment of the organization

Organizational Development Interventions In Learning Organizations

The purpose of this article was to demonstrate that organizational development interventions in key areas of learning organizations assist to further develop such organizations because they are open systems and accustomed to planned changes. Therefore, their resistance to planned developmental changes is limited in comparison to non-learning organizations that are not accustomed to this process. The ultimate goal of organization development is to make the organization more open and more adaptive through increases in capability and potential in order for it to continue making such planned change efforts on an action orientation basis. Learning organizations are viable and vital means for developing an organization’s culture of high performance learners who become transformed people much better adapted to get results that affect the bottom line and the quality of life in their organizations. The author of this article focused organizational development interventions on a number of key areas in learning organizations which are: human resources policies and procedures, evaluation of human resources, structure and design, training and development of human resources, communication, and leadership. In this article, the above cited areas are referred to as concentrations. The organizational development intervention process consists of the diagnosis in order to identify the elements to be evaluated in the areas of concentration; the presentation of the results of the diagnoses in proposals for the implementation of the results; and the implementation through planned change efforts

Absence Of Transformational Leadership In Greek Enterprises Results In The Inability Of Forming Learning Organizations

Transactional leadersemploy transactions in which they use their legitimate reward and coercivepowers to give commands and exchange rewards for services rendered. Transformationalleadership makes subordinates aware of the importance of their jobs andperformance to the organization as well as to their own needs for personalgrowth which precipitates motivation for them to work for the good of theorganization. Learning organizations are characterized by total employeeinvolvement in a process that is collaboratively conducted and collectively accountablewithin a planned and meaningful change that is directed toward shared values orprinciples. Traditional organizations exist within stable environments, havevertical structures, and have a strategy that is formulated at the top. Additionally,they have a centralized decision-making process; tasks are rigidly defined andspecialized; the organizational culture is rigid and resistant to change; andthey have formal systems of filtered communication pivoting around the verticalhierarchy. Learning organizations cannot be formed in the Greek privatebusiness sector because the leadership of said sector is not transformational.Greece failed to develop an advanced industrial complex because of the largenumber of small enterprises in the form of proprietorships and partnershipsthat have dominated the economy. Additionally, Greek industry experienced the profound absence of thecorporate form of business that necessitates medium and large businessenterprises for the attainment of effective and efficient factors of productionand economies of scale that precipitate transformational leadership and learningorganizations