This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Goedel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy.

This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium.

This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.

Sometimes in this life it may seem as if we are at the end of our rope, that all hope is lost. We feel as if we're stuck in our situation and there's no way out. It seems that everything in your life is going downhill. It is important for us to learn that situations and circumstances sometimes come as a test of our faithfulness. You will find between these pages keys to understanding that no matter what the situation or circumstance, you must not throw in the towel; you must not give up the fight, because it's not over until it's over. Though the road seems dark, keep moving on, because the greater the struggle the greater the reward. The greater the suffering the greater the blessing