Title
Studies in Weak Arithmetics, Volume 1 (Volume 1) (Lecture Notes),Used
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The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. In this volume, after a general presentation of weak arithmetics, the following topics are studied: the properties of integers of a real closed field equipped with exponentiation; conservation results for the induction schema restricted to firstorder formulas with a finite number of alternations of quantifiers; a survey on a class of tools called pebble games; the fact that the reals e and pi have approximations expressed by firstorder formulas using bounded quantifiers; properties of infinite pictures depending on the universe of sets used; a language that simulates in a sufficiently nice manner all algorithms of a certain restricted class; the logical complexity of the axiom of infinity in some variants of set theory without the axiom of foundation; and the complexity to determine whether a trace is included in another one.
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Frequently Asked Questions
- Q: What is the main focus of 'Studies in Weak Arithmetics, Volume 1'? A: The book primarily focuses on the application of logical methods to number theory, exploring various topics within the field of weak arithmetics.
- Q: Who is the author of this book? A: 'Studies in Weak Arithmetics, Volume 1' is authored by Patrick Cégielski.
- Q: How many pages does the book contain? A: The book contains a total of 221 pages.
- Q: What is the binding type of this book? A: This book is available in paperback binding.
- Q: When was 'Studies in Weak Arithmetics, Volume 1' published? A: The book was published on December 15, 2009.
- Q: What topics are covered in 'Studies in Weak Arithmetics, Volume 1'? A: The book covers topics such as properties of integers in real closed fields, conservation results for induction schemas, and the logical complexity of the axiom of infinity among others.
- Q: Is there any specific audience for this book? A: This book is suitable for mathematicians, philosophers, and theoretical computer scientists interested in the logical foundations of number theory.
- Q: Does this book include any illustrations or graphs? A: The product details do not specify the inclusion of illustrations or graphs.
- Q: Is there a specific edition of this book? A: The details provided do not mention any special edition for this volume.
- Q: What is the significance of weak arithmetics as discussed in the book? A: Weak arithmetics represent an important intersection of logic and number theory, providing insights into mathematical properties and computational methods.