Theorien der reellen Zahlen und Interpretierbarkeit

Daniel Alscher

Published by De Gruyter 2016

Theorien der reellen Zahlen und Interpretierbarkeit

Theories of Real Numbers and Interpretability

Daniel Alscher

Volume 25 in the series Logos

https://doi.org/10.1515/9783110459197

Overview
Contents

About this book

In contrast to the importance of real numbers for mathematical sciences a metamathematical approach to real numbers has never been developed systematically, a gap this book undertakes to fill. The investigated formal theories of real numbers are based on the theory of real closed fields, due to Tarski known as a complete theory. Theory extensions are considered by adding different set-theoretical or arithmetical concepts, like a pairing function, a predicate for natural numbers or second-order logic. To capture the special features of the metamathematics of real numbers the intertheoretical relation of interpretability is presented and examined, particularly slight variations on the common definition that allow a more accurate classification of the theories of real numbers. Thus the main theorems proven in this book are positive and negative propositions about the interpretability of and in theories of real numbers, constituting a hierarchy among them and comparing them with other canonical mathematical theories. Philosophically the results determine the resources that are employed in these theories and establish a reducibility approach to real numbers inspired by Hilbert's philosophy of mathematics.

Author / Editor information

Daniel Alscher, Berlin.

Topics

Frontmatter Publicly Available Download PDF	I
Vorwort Requires Authentication Unlicensed Licensed Download PDF	V
Inhalt Publicly Available Download PDF	VII
Einleitung Requires Authentication Unlicensed Licensed Download PDF	1
1. Interpretierbarkeit Requires Authentication Unlicensed Licensed Download PDF	15
2. Die Theorie der reell abgeschlossenen Körper RCF Requires Authentication Unlicensed Licensed Download PDF	63
3. Negative Resultate über Interpretierbarkeit in RCF Requires Authentication Unlicensed Licensed Download PDF	80
4. Interpretierbarkeit zwischen Theorien von Körpern Requires Authentication Unlicensed Licensed Download PDF	98
5. Arithmetisierung der Geometrie Requires Authentication Unlicensed Licensed Download PDF	107
6. Eine erststufige Theorie reeller und natürlicher Zahlen Requires Authentication Unlicensed Licensed Download PDF	133
7. Zweitstufige Theorien der reellen Zahlen Requires Authentication Unlicensed Licensed Download PDF	156
Schluss Requires Authentication Unlicensed Licensed Download PDF	192
Anhang Requires Authentication Unlicensed Licensed Download PDF	225
Literatur Requires Authentication Unlicensed Licensed Download PDF	259
Sachregister Requires Authentication Unlicensed Licensed Download PDF	265

(Deutsch)

Language: German
Publisher: De Gruyter
Audience: Scholars, libraries, academic institutions, mathematicians
Pages
- Front matter: 8
- Main content: 266
Keywords: Hilbert; David; solids; algebra; interpretation

eBook

Published: January 15, 2016
ISBN: 9783110459197

Hardcover

Published: January 15, 2016
ISBN: 9783110458565