The tragic loss caused by the premature death of Abraham Robinson brought about a deeply felt desire by his close friends, colleagues, and pupils to commemorate his exceptional gifts and personality. An appropriate way to accomplish this appeared to be the selection and editing of his writings on applied mathematics, mathematics, mathematical logic, philosophy, and nonstandard analysis, and the publication of these papers in these volumes.
This edition presents only an incomplete picture of Robinson’s work and influence on mathematics and mathematical logic. It is impossible to do full justice to his many lectures, his philosophical and expository articles, and his many contributions to the work of his pupils. We do feel, however, that the present selection, together with his many important books and monographs, will show the mark his work has left on the development of mathematics and mathematical logic in this century.
Author(s): H.J.Keisler, S.Körner, W.A.J.Luxemburg, A.D.Young (eds)
Publisher: North-Holland
Year: 1979
Language: English
Commentary: Scanned by Envoy
Pages: 582
City: Amsterdam
Abraham Robinson: Selected papers. Volume 2. Nonstandard Analysis and Philosophy ......Page 1
Photo: Abraham Robinson (1970) ......Page 3
Editors' Note ......Page 8
Table of contents ......Page 10
Biography of Abraham Robinson (George B. Seligman) ......Page 12
Introduction to Papers on Nonstandard Analysis and Analysis (W. A. J. Luxemburg) ......Page 32
Introduction to Papers on Philosophy (S. Korner) ......Page 42
Part I. Nonstandard Analysis and Analysis ......Page 48
Non-standard Analysis ......Page 50
On Languages Which Are Based on Non-standard Arithmetic ......Page 59
On Generalized Limits and Linear Functionals ......Page 94
On the Theory of Normal Families ......Page 109
Solution of an Invariant Subspace Problem of K. T. Smith and P. R. Halmos (with Allen R. Bernstein) ......Page 135
Topics in Non-archimedean Mathematics ......Page 146
A New Approach to the Theory of Algebraic Numbers ......Page 160
A New Approach to the Theory of Algebraic Numbers, II ......Page 164
Non-standard Theory of Dedekind Rings ......Page 169
Nonstandard Arithmetic ......Page 179
On Some Applications of Model Theory to Algebra and Analysis ......Page 205
Topics in Nonstandard Algebraic Number Theory ......Page 236
A Set-Theoretical Characterization of Enlargements (with Elias Zakon) ......Page 253
Germs ......Page 267
Elementary Embeddings of Fields of Power Series ......Page 279
Compactification of Groups and Rings and Nonstandard Analysis ......Page 290
Algebraic Function Fields and Non-standard Arithmetic ......Page 303
The Nonstandard λ:ϕ(x): Model. I. The Technique of Nonstandard Analysis in Theoretical Physics (with Peter J. Kelemen) ......Page 317
The Nonstandard λ:ϕ(x): Model. II. The Standard Model from a Nonstandard Point of View (with Peter J. Kelemen) ......Page 322
A Limit Theorem on the Cores of Large Standard Exchange Economies (with Donald J. Brown) ......Page 326
Function Theory on Some Nonarchimedean Fields ......Page 330
Nonstandard Points on Algebraic Curves ......Page 353
Enlarged Sheaves ......Page 380
The Cores of Large Standard Exchange Economies (with Donald J. Brown) ......Page 392
Nonstandard Exchange Economies (with Donald J. Brown) ......Page 402
On the Finiteness Theorem of Siegel and Mahler Concerning Diophantine Equations (with P. Roquette) ......Page 417
Standard and Nonstandard Number Systems ......Page 473
On the Integration of Hyperbolic Differential Equations ......Page 492
On Functional Transformations and Summability ......Page 501
Core-consistency and Total Inclusion for Methods of Summability (with G. G. Lorentz) ......Page 530
Part II. Philosophy ......Page 538
On Constrained Denotation ......Page 540
Formalism 64 ......Page 552
Model Theory ......Page 571
The Metaphysics of the Calculus ......Page 584
Concerning Progress in the Philosophy of Mathematics ......Page 603
Some Thoughts on the History of Mathematics ......Page 615
Bibliography ......Page 622
Doctoral Students of Abraham Robinson ......Page 629
