Studies in Weak Arithmetics
Seiten
2009
Centre for the Study of Language & Information (Verlag)
978-1-57586-602-4 (ISBN)
Centre for the Study of Language & Information (Verlag)
978-1-57586-602-4 (ISBN)
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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. This title offers a general presentation of weak arithmetics.
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 first-order 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 first-order 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.
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 first-order 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 first-order 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.
Patrick Cegielski is professor at Universite Paris-Est Creteil-IUT de Senart Fontainebleau.
| Erscheint lt. Verlag | 10.8.2010 |
|---|---|
| Reihe/Serie | Lecture Notes |
| Verlagsort | Stanford |
| Sprache | englisch |
| Maße | 16 x 23 mm |
| Gewicht | 312 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 1-57586-602-1 / 1575866021 |
| ISBN-13 | 978-1-57586-602-4 / 9781575866024 |
| Zustand | Neuware |
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