Ebook: The Collected Works of J. Richard Büchi

J. Richard Biichi is well known for his work in mathematical logic and theoretical computer science. (He himself would have sharply objected to the qualifier "theoretical," because he more or less identified science and theory, using "theory" in a broader sense and "science" in a narrower sense than usual.) We are happy to present here this collection of his papers. I (DS)1 worked with Biichi for many years, on and off, ever since I did my Ph.D. thesis on his Sequential Calculus. His way was to travel locally, not globally: When we met we would try some specific problem, but rarely dis­ cussed research we had done or might do. After he died in April 1984 I sifted through the manuscripts and notes left behind and was dumbfounded to see what areas he had been in. Essentially I knew about his work in finite au­ tomata, monadic second-order theories, and computability. But here were at least four layers on his writing desk, and evidently he had been working on them all in parallel. I am sure that many people who knew Biichi would tell an analogous story.

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Contents: The Person and His Work.- The Publications, with Comments.

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Contents: The Person and His Work.- The Publications, with Comments.
Content:
Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Association for Symbolic Logic....Pages 2-3
The Life of J. Richard B?chi....Pages 4-6
The Work of J. Richard B?chi....Pages 7-17
The Role of B?chi’s Automata in Computing Science....Pages 18-22
J. Richard B?chi’s Doctoral Students....Pages 23-23
Front Matter....Pages 27-27
Die Boole’sche Partialordnung und die Paarung von Geff?gen....Pages 33-101
Representation of Complete Lattices by Sets....Pages 103-119
Investigation of the Equivalence of the Axiom of Choice and Zorn’s Lemma from the Viewpoint of the Hierarchy of Types....Pages 121-139
Skolem Rings and Their Varieties....Pages 161-221
On the existence of totally heterogeneous spaces....Pages 141-146
Jordan Circuits of a Graph....Pages 147-159
Skolem Rings and Their Varieties....Pages 161-221
The Theory of Proportionality as an Abstraction of Group Theory....Pages 226-232
Invariants of the Anti-Automorphisms of a Group....Pages 234-240
Model Theoretic Approaches to Definability....Pages 241-250
Definibility in Normal Theories....Pages 252-260
Variations on a Theme of Cantor in the Theory of Relational Structures....Pages 261-276
Relatively Categorical and Normal Theories....Pages 277-286
Mathematische Theorie des Verhaltens endlicher Automaten....Pages 295-302
Regular Canonical Systems....Pages 317-337
Algebraic Theory of Feedback in Discrete Systems, Part I....Pages 338-369
Front Matter....Pages 27-27
Canonical Systems which Produce Periodic Sets....Pages 371-380
Weak Second-Order Arithmetic and Finite Automata....Pages 398-424
On a Decision Method in Restricted Second Order Arithmetic....Pages 425-435
Transfinite Automata Recursions and Weak Second Order Theory of Ordinals....Pages 437-457
Decision Methods in the Theory of Ordinals....Pages 459-462
Definability in the Monadic Second-Order Theory of Successor....Pages 464-468
The Complete Extensions of the Monadic Second Order Theory of Countable Ordinals....Pages 469-492
Solving Sequential Conditions by Finite-State Strategies....Pages 493-516
Algorithmisches Konstruieren von Automaten und Die Herstellung von Gewinnstrategien Nach Cantor-Bendixson....Pages 525-541
On the Presentation of Winning Strategies via the Cantor-Bendixson Method....Pages 543-556
Using Determinancy of Games to Eliminate Quantifiers....Pages 567-580
Turing-Machines and the Entscheidungsproblem....Pages 581-592
Recursive Definition and Complexity of Functions Over Arbitrary Data Structures....Pages 593-620
Coding in the Existential Theory of Concatenation....Pages 627-639
Definability in the Existential Theory of Concatenation and Undecidable Extensions of this Theory....Pages 641-663
Large Convex Sets in Oriented Matroids....Pages 665-670
....Pages 671-683