Ebook: Aspects of Incompleteness

This book presents some of the main areas and results of general metamathematics. In addition to standard results of G?del et al. on incompleteness, (non-)finite axiomatizability, interpretability, etc., it contains a thorough treatment of partial conservativity and degrees of interpretability. The method of arithmetization plays an all important role in the book. The reader is assumed to be acquainted with this method and with the elements of recursion theory. The book will be useful as a textbook for a graduate student course - there are many exercises - and as a reference text for researchers.

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This book presents some of the main areas and results of general metamathematics. In addition to standard results of G?del et al. on incompleteness, (non-)finite axiomatizability, interpretability, etc., it contains a thorough treatment of partial conservativity and degrees of interpretability. The method of arithmetization plays an all important role in the book. The reader is assumed to be acquainted with this method and with the elements of recursion theory. The book will be useful as a textbook for a graduate student course - there are many exercises - and as a reference text for researchers.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-4
Preliminaries....Pages 5-22
Incompleteness....Pages 23-41
Numerations of R.E. Sets....Pages 42-51
Axiomatizations....Pages 52-61
Partial Conservativity....Pages 62-74
Interpretability....Pages 75-93
Degrees of Interpretability....Pages 94-118
Generalizations....Pages 119-124
Back Matter....Pages 125-135

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This book presents some of the main areas and results of general metamathematics. In addition to standard results of G?del et al. on incompleteness, (non-)finite axiomatizability, interpretability, etc., it contains a thorough treatment of partial conservativity and degrees of interpretability. The method of arithmetization plays an all important role in the book. The reader is assumed to be acquainted with this method and with the elements of recursion theory. The book will be useful as a textbook for a graduate student course - there are many exercises - and as a reference text for researchers.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-4
Preliminaries....Pages 5-22
Incompleteness....Pages 23-41
Numerations of R.E. Sets....Pages 42-51
Axiomatizations....Pages 52-61
Partial Conservativity....Pages 62-74
Interpretability....Pages 75-93
Degrees of Interpretability....Pages 94-118
Generalizations....Pages 119-124
Back Matter....Pages 125-135
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