The Annotated Gel: A Reader's Guide to his Classic Paper on Logic and Incompleteness (Paperback) (ISBN-13: 9798986414201)

The Annotated Gel offers a guided tour of Kurt Gel's 1931 article on incompleteness, which demonstrated unexpected limits to the power of many logical systems. Today we call these results Gel's First and Second Incompleteness Theorems. The book includes the complete article in a new English translation, interleaved with commentary that guides the reader through Gel's work, step by step.

The commentary concentrates on Gel's exposition. It describes what he is doing at each point, and how it relates to other parts of the article. It elaborates on his proofs by outlining them, for example, or by making a table of his variables and their uses, or by filling in gaps in his arguments.

The translation uses modern mathematical notation and terminology. It replaces Gel's function and relation names, based on German word fragments, with English equivalents. Its language is less formal than that of the existing translations, which date from the 1960s.

The book assumes some familiarity with mathematical definitions and proofs, at the level of an undergraduate abstract math course, as well as some knowledge of formal logic, from an introductory course or the equivalent.