Tags
Language
Tags
March 2024
Su Mo Tu We Th Fr Sa
25 26 27 28 29 1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31 1 2 3 4 5 6

Development of Mathematical Logic

Posted By: arundhati
Development of Mathematical Logic

R. L. Goodstein, "Development of Mathematical Logic"
1971 | ISBN-10: 0236176692 | 150 pages | Djvu | 2 MB

PREFACE
Formal logic has a long history which goes back at least to the time of Aristotle. It appears to have suffered long periods of neglect, although recent research has shown that there was a flowering of logical studies during the Middle Ages. The remarkable expansion of the subject which has been so conspicuous a feature of the present century had its roots, however, in the nineteenth century in the pioneer work of George Boole, Augustus de Morgan and above all Gotlob Frege.
The present account concentrates upon some of the themes which have shaped the development of mathematical logic during the past forty years. In particular we consider the great discoveries of T. Skolem, Kurt Godel and Gerhart Gentzen which have played so decisive a role during this period. Some of these results, like Godel's proof of the incompleteness of formalised arithmetic, are presented in considerable detail, whereas others, like Gentzen's consistency proof for formalised arithmetic are described in outline only.
Many topics have been omitted entirely, for instance modal logic, the axiomatisation of many-value logics, and the important new constructive
logic of A. A. Markov and N. A. Shanin which lies between classical logic and Brouwer's intuitionistic logic. I have omitted also all reference to the new constructive systems of analysis, which owe their development in this century to Brouwer's critique of logic, like my own system of recursive analysis or the very extensive work of the Leningrad school, under the guidance of Markov and Shanin.
Even in those areas of mathematical logic which I have discussed in the book I do not wish to be thought to claim that everything that is mentioned
is thereby held to be more important than anything which is not, for this is certainly not the case. I have consciously included a few relatively minor results either because they complete some line of enquiry which has particularly interested me or because they are of unusual elegance and simplicity.
I should like to express my thanks to Mr. J. G. Mordue of Logos Press for his advice and assistance in the preparation of this book and to Bell and Bain Ltd., the printers, for the excellence of their work.
R. L. GOODSTEIN, University of Leicester, January 1971