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What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner.
To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin''s problems on projective sets using determinacy of infinite games and large cardinals.
Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
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This book deals with the dynamics of local-level politics in China and India. China introduced new policies to restructure local politics in 1978. In place of communes, civil society organizations and cooperatives were introduced in villages. More changes came about with the introduction of the Organic Law of the Villagers'' Committees of the People''s Republic of China in 1998. The new local power structure includes state-sponsored institutions like Villagers Committees and the traditional civil society organizations (CSOs) and non-government organizations (NGOs). As in China, local politics in India undergoes considerable changes during the last few decades. Panchayati Raj Institutions (PRIs) were reformed in 1992 with a constitutional amendment act. CSOs and NGOs were allowed to function. Against this background, the present book is undertaken with the objectives first, to present two different models of local politics and second, to compare the two, finally to focus on the two different models of development. This book will interest scholars of rural governance, rural transformation, and the role of the grassroots CSOs and NGOs in shaping development program and growth in the two large countries in Asia.
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