In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of mathematics can be reduced to set theory. He explains concepts and results of recursion theory in intuitive terms, and reaches the limitative results of Skolem, Tarski, Church and Godel (the celebrated incompleteness theorems). For students of mathematics and philosophy, this book provides an excellent introduction to logic and set...
In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel ...
Both theoretical and empirical aspects of single- and multi-winner voting procedures are presented in this collection of papers. Starting from a discussion of the underlying principles of democratic representation, the volume includes a description of a great variety of voting procedures. It lists and illustrates their susceptibility to the main voting paradoxes, assesses (under various models of voters' preferences) the probability of paradoxical outcomes, and discusses the relevance of the theoretical results to the choice of voting system.
Both theoretical and empirical aspects of single- and multi-winner voting procedures are presented in this collection of papers. Starting from a discu...
