Backgrounds of Arithmetic and Geometry: An Introduction

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World Scientific, 1995 - Mathematics - 286 pages
The book is an introduction to the foundations of Mathematics. The use of the constructive method in Arithmetic and the axiomatic method in Geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link with the study of real numbers and algebraic structures.
 

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Contents

PREFACE
1
ARITHMETIC
18
AXIOMATIC THEORIES
48
ALGEBRAIC BASES OF GEOMETRY
63
THE BASES OF EUCLIDEAN GEOMETRY
87
BIRKHOFFS AXIOMATIC SYSTEM
122
GEOMETRICAL TRANSFORMATIONS
139
THE ERLANGEN PROGRAM
167
BACHMANNS AXIOMATIC SYSTEM Francise Radó
236
HINTS
253
BIBLIOGRAPHY
261
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