At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.
There is a new age of philanthropy in Europe: a 50 billion-plus financial market. New wealth, growing social need, and innovations in finance are creating a revolution in how people give. In this detailed, how-to guide to researching philanthropy in Europe, Christopher Carnie maps these changes, focusing on major donors--people and foundations investing or donating 25,000 or mroe--to help readers find their way around this transforming sector. Looking across the continent, How Philanthropy Is Changing in Europe includes interviews with philanthropists, wealth managers, and fundraisers that shed light on key segments of European philanthropy, such as the role of women. Carnie also draws on new giving data to provide practical insider knowledge on how to access donors and donor information. Complete with a substantial appendix of sources, this book not only helps readers to understand the revolution in philanthropy in Europe, but also supplies crucial market information for anyone building their own fundraising or philanthropy strategies.
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