The logical and mathematical results presented in this book are not at all due to the author, except perhaps for some minor simplifications and observations. There are some references in the text to the people who have created and developed the subject of Gödelian extensions of theories, but I'm aware that there are many others who could have been mentioned, and I ask their indulgence for my casual style of presentation. The contribution of the book consists in a sustained presentation, starting from basic concepts, of a particular view of the topic of Gödelian extensions. It is my optimistic hope that philosophers, mathematicians, and others with an interest in this topic will find the book helpful in acquring a basic grasp of the philosophical and logical results and issues.

Writing this book, over the past couple of years, was made possible through the facilities and pleasant working environment offered by the computer science department at Luleå University of Technology. Several people have commented on the text, and I am grateful in particular to Sam Buss, Calvin Ostrum, Charles Silver, Walter Felscher, Leon Horsten, Damjan Bojadziev, and Alex Blum for useful comments.

Marcia, my wife, hasn't commented on the book except to say “That's very nice, dear”, but must nevertheless be held partly responsible for its contents, in that she, through a series of strange and wonderful events, separated me from a slothlike bachelor existence, causing me to do all sorts of things, like finding a job and writing a book. I also choose to conveniently hold her responsible for any remaining mistakes in the book.