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The author follows a year in the life of the Northern Cardinal with fact-filled text and glowing color photographs. Full of intriguing facts, the book also recounts how cardinals cope with predators and parasites, serve as surrogate parents for other species, and survive adverse weather and shortages of food. For backyard bird watchers, she suggests ways to attract cardinals and gives recipes for cardinal foods.
This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book [Sh5] and to the article by M. R. Burke and M. Magidor [BM] which also initiated our students' interest for Shelah's pcf-theory.
From 1900 through 2000, the Catholic Church has had nine popes. As the 21st century began, John Paul II was in his 22nd year as head of the church. During the century more than 600 cardinals have helped to lead the church. This biographical reference work covers all nine popes and all 641 cardinals. The first section presents the popes in chronological order and provides date and place of birth and death, education and training for the priesthood, positions held within the church, and roles in church leadership and various conclaves. In the second section the cardinals are listed alphabetically and much the same biographical information is provided for them. (An appendix gives all the cardinals appointed by John Paul II in 2001.)
Drawing on more than a hundred interviews with Vatican officials, this book affords a firsthand look at the people, the politics, and the organization behind the institution. Throughout, revealing and colorful anecdotes from church history and the present day bring the unique culture of the Vatican to life.
From Pythagoreans to Hegel, and beyond, this book gives a brief overview of the history of the notion of graphs and introduces the main concepts of graph theory in order to apply them to philosophy. In addition, this book presents how philosophers can use various mathematical notions of order. Throughout the book, philosophical operations and concepts are defined through examining questions relating the two kinds of known infinities – discrete and continuous – and how Woodin's approach can influence elements of philosophy. We also examine how mathematics can help a philosopher to discover the elements of stability which will help to build an image of the world, even if various approaches (for example, negative theology) generally cannot be valid. Finally, we briefly consider the possibilities of weakening formal thought represented by fuzziness and neutrosophic graphs. In a nutshell, this book expresses the importance of graphs when representing ideas and communicating them clearly with others.
A complete and updated commentary on the Code of Canon Law prepared by the leading canonists of North America and Europe. Contains the full, newly translated text of the Code itself as well as detailed commentaries by thirty-six scholars commissioned by the Canon Law Society of America.
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