A Course in Mathematical Logic

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Springer Science & Business Media, 1977 - Mathematics - 286 pages
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This book is a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses; they include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a sub-class of von Neumann's universe, the Kolmogorov theory of complexity. Feferman's theorem on Goedel formulas as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations. A number of informal digressions concerned with psychology, linguistics, and common sense logic should interest students of the philosophy of science or the humanities.
 

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Contents

II
3
III
20
IV
103
V
149
VI
175
VII
177
VIII
206
IX
231
X
233
XI
261
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Advanced Mathematical Thinking
David Tall
No preview available - 1994
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About the author (1977)

Neal Koblitz is a Professor of Mathematics at the University of Washington in the Department of Mathematics. He is also an adjunct professor with the Centre for Applied Cryptographic Research at the University of Waterloo. He is the creator of hyperelliptic curve cryptography and the independent co-creator of elliptic curve cryptography. Professor Koblitz received his undergraduate degree from Harvard University, where he was a Putnam Fellow, in 1969. He received his Ph.D. from Princeton University in 1974 under the direction of Nickolas Katz.

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