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: 694
City: Amsterdam
Abraham Robinson: Selected papers. Volume 1. Model Theory and Algebra ......Page 1
Photo: Abraham Robinson in Brasilia (1972) ......Page 3
Editors’ Note ......Page 8
Table of contents ......Page 10
Facsimile of first MS page of University of London thesis ......Page 13
Biography of Abraham Robinson (George B. Seligman) ......Page 14
Introduction (H. J. Keisler) ......Page 34
Part I. Expository Papers ......Page 40
On the Application of Symbolic Logic to Algebra ......Page 42
Recent Developments in Model Theory ......Page 51
On the Construction of Models ......Page 71
Metamathematical Problems ......Page 82
Model Theory as a Framework for Algebra ......Page 99
Part II. Pure Model Theory ......Page 124
A Result on Consistency and Its Application to the Theory of Definition ......Page 126
Ordered Structures and Related Concepts ......Page 138
Note on a Problem of L. Henkin ......Page 144
Completeness and Persistence in the Theory of Models ......Page 147
Syntactical Transforms (with A. H. Lightstone) ......Page 159
Relative Model-Completeness and the Elimination of Quantifiers ......Page 185
Obstructions to Arithmetical Extension and the Theorem of Łoś and Suszko ......Page 199
Model Theory and Non-standard Arithmetic ......Page 206
Forcing in Model Theory ......Page 244
Completing Theories by Forcing (with Jon Barwise) ......Page 258
Infinite Forcing in Model Theory ......Page 282
Inductive Theories and Their Forcing Companions {with Edward R. Fisher) ......Page 306
Nonstandard Arithmetic and Generic Arithmetic ......Page 319
Generic Categories ......Page 337
A Note on Topological Model Theory ......Page 346
Part III. Applications of Model Theory to Algebra ......Page 360
On Axiomatic Systems Which Possess Finite Models ......Page 361
On Predicates in Algebraically Closed Fields ......Page 371
Note on an Embedding Theorem for Algebraic Systems ......Page 383
Metamathematical Considerations on the Relative Irreducibility of Polynomials (with P. C. Gilmore) ......Page 387
On Ordered Fields and Definite Functions ......Page 394
Further Remarks on Ordered Fields and Definite Functions ......Page 409
Some Problems of Definability in the Lower Predicate Calculus ......Page 414
On the Representation of Herbrand Functions in Algebraically Closed Fields (with A. H. Lightstone) ......Page 435
Solution of a Problem of Tarski ......Page 453
On the Concept of a Differentially Closed Field ......Page 479
Elementary Properties of Ordered Abelian Groups (with Elias Zakon) ......Page 495
A Note on Embedding Problems ......Page 510
On the Notion of Algebraic Closedness for Noncommutative Groups and Fields ......Page 517
On Bounds in the Theory of Polynomial Ideals ......Page 521
A Decision Method for Elementary Algebra and Geometry — Revisited ......Page 529
Algorithms in Algebra ......Page 543
Part IV. Pure Algebra ......Page 560
On Nil-Ideals in General Rings ......Page 562
On a Certain Variation of the Distributive Law for a Commutative Algebraic Field ......Page 564
The Characterization of Algebraic Plane Curves (with Th. Motzkin) ......Page 573
On Non-Associative Systems ......Page 590
Solution of a Problem by Erdös-Gillman-Henricksen ......Page 598
Local Differential Algebra ......Page 600
Local Partial Differential Algebra (with S. Halfin) ......Page 630
On the Real Closure of a Hardy Field ......Page 646
Ordered Differential Fields ......Page 653
Part V. IBM Papers ......Page 664
Random-Access Stored-Program Machines, an Approach to Programming Languages (with Calvin C. Elgot) ......Page 666
Multiple Control Computer Models (with C. C. Elgot and J. D. Rutledge) ......Page 701
Some Remarks on Threshold Functions ......Page 718
Bibliography ......Page 726
Doctoral Students of Abraham Robinson ......Page 733
