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140122  eng 
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a 9781475744897

100 
1 

a Barnes, D.W.

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0 
0 
a An Algebraic Introduction to Mathematical Logic
h Elektronische Ressource
c by D.W. Barnes, J.M. Mack

250 


a 1st ed. 1975

260 


a New York, NY
b Springer New York
c 1975, 1975

300 


a IX, 123 p
b online resource

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0 

a I Universal Algebra  II Propositional Calculus  III Properties of the Propositional Calculus  IV Predicate Calculus  V FirstOrder Mathematics  VI ZermeloFraenkel Set Theory  VII Ultraproducts  VIII NonStandard Models  IX Turing Machines and Gödel Numbers  X Hilbert’s Tenth Problem, Word Problems  References and Further Reading  Index of Notations

653 


a Mathematical logic

653 


a Algebra

653 


a Mathematical Logic and Foundations

700 
1 

a Mack, J.M.
e [author]

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0 
7 
a eng
2 ISO 6392

989 


b SBA
a Springer Book Archives 2004

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0 

a Graduate Texts in Mathematics

028 
5 
0 
a 10.1007/9781475744897

856 
4 
0 
u https://doi.org/10.1007/9781475744897?nosfx=y
x Verlag
3 Volltext

082 
0 

a 511.3

520 


a This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the metaIanguage. We are not attempting to construct a foundation on which all mathematics is to be basedrather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory
