Inexhaustibility: A Non-Exhaustive Treatment (Lecture Notes in Logic Book 16) by Torkel Franzén (PDF)

Description

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel’s incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you’ve heard of Goedel’s Incompleteness theorem and ever wondered why we can’t just keep adding the axiom “this system is consistent”, this is the book for you! The culmination of this book is to answer the question “If we really believe the axioms of Peano arithmetic, how far can we extend them based solely on this belief?” Along the way, you’ll learn about ordinals, recursion theory, and various systems of axioms.This book assumes very little background, and proceeds at a gentle pace. Concepts are well explained (something “serious” math books often lack!), so it’s very readable. If you have much mathematical background, there will probably be several chapters you can skip.That said, this is not for the mathematically faint of heart: metamathematics, by its nature, requires some mathematical aptitude and comfort with abstract concepts. If the proof of Goedel’s theorem frightens you, most of the later chapters of this book will be equally unapproachable. But if you liked Goedel’s theorem and want to know more, this book is highly recommended.

⭐An extremely interesting followup to his book on Godel’s proof. Unfortunately his last, as he died at the very young age of 55 (or so)

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