



LEADER 
03089nmm a2200409 u 4500 
001 
EB000720738 
003 
EBX01000000000000000573820 
005 
00000000000000.0 
007 
cr 
008 
140122  eng 
020 


a 9789401582483

100 
1 

a Ehrlich, P.
e [editor]

245 
0 
0 
a Real Numbers, Generalizations of the Reals, and Theories of Continua
h Elektronische Ressource
c edited by P. Ehrlich

250 


a 1st ed. 1994

260 


a Dordrecht
b Springer Netherlands
c 1994, 1994

300 


a XXXII, 288 p
b online resource

505 
0 

a The Late 19thCentury Geometrical Motivation  Veronese’s NonArchimedean Linear Continuum  Review of Hilbert’s Foundations of Geometry (1902): Translated for the American Mathematical Society by E. V. Huntington (1903)  On NonArchimedean Geometry. Invited Address to the 4th International Congress of Mathematicians, Rome, April 1908. Translated by Mathieu Marion (with editorial notes by Philip Ehrlich)  IV. Extensions and Generalizations of the Reals: Some 20thCentury Developments  Calculation, Order and Continuity  The Hyperreal Line  All Numbers Great and Small  Rational and Real

653 


a Philosophy of Science

653 


a Mathematical logic

653 


a Logic

653 


a Mathematical Logic and Foundations

653 


a Logic

653 


a History of Mathematical Sciences

653 


a History

653 


a Philosophy and science

653 


a Algebra

653 


a Order, Lattices, Ordered Algebraic Structures

653 


a Mathematics

653 


a Ordered algebraic structures

710 
2 

a SpringerLink (Online service)

041 
0 
7 
a eng
2 ISO 6392

989 


b SBA
a Springer Book Archives 2004

490 
0 

a Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science

856 


u https://doi.org/10.1007/9789401582483?nosfx=y
x Verlag
3 Volltext

082 
0 

a 511.3

520 


a Since their appearance in the late 19th century, the CantorDedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as nonArchimedean geometry, nonstandard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction
