The Collected Works of J. Richard Büchi

ISBN-13: 9781461389309 / Angielski / Miękka / 2011 / 696 str.

J. Richard B. Chi; Saunders Mac Lane; Dirk Siefkes

Opis

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."

Spis treści

1. The Person and His Work.- J. Richard Büchi (1924–1984).- The Life of J. Richard Büchi.- The Work of J. Richard Büchi.- The Role of Büchi’s Automata in Computer Science.- J. Richard Büchi’s Doctoral Students.- Abstracts Published by J. Richard Büchi.- 2. The Publications, with Comments.- Section 1. Boolean Algebras.- [1] Die Boole’sche Partialordnung und die Paarung von Gefügen.- [2] Representation of Complete Lattices by Sets.- [3] Investigation of the Equivalence of the Axiom of Choice and Zorn’s Lemma from the Viewpoint of the Hierarchy of Types.- Section 2. Discrete Spaces.- [4] On the Existence of Totally Heterogeneous Spaces.- [19] Jordan Circuits of a Graph (with Gary Haggard).- [37] Skolem Rings and Their Varieties (with T. Michael Owens).- Section 3. Towards a Theory of Definability.- [5] The Theory of Proportionality as an Abstraction of Group Theory (with Jesse B. Wright).- [6] Invariants of the Anti-Automorphisms of a Group (with Jesse B. Wright).- [21] Model Theoretic Approaches to Definability.- [22] Definability in Normal Theories (with Kenneth J. Danhof).- [23] Variations on a Theme of Cantor in the Theory of Relational Structures.- [40] Relatively Categorical and Normal Theories.- Abstract 11. Relatively Categorical and Normal Theories.- Section 4. Automata and Grammars.- [10] Mathematische Theorie des Verhaltens endlicher Automaten.- Mathematical Theory of the Behavior of Finite Automata (English translation by Sylvia Büchi, Peter Deussen, and Dirk Siefkes).- [11] Regular Canonical Systems.- [12] Algebraic Theory of Feedback in Discrete Systems.- [17] Canonical Systems which Produce Periodic Sets (with William H. Hosken).- Section 5. Automata and Monadic Theories.- [7] Weak Second-Order Arithmetic and Finite Automata.- [8] On a Decision Method in Restricted Second Order Arithmetic.- [13] Transfinite Automata Recursions and Weak Second Order Theory of Ordinals.- [14] Decision Methods in the Theory of Ordinals.- [16] Definability in the Monadic Second-Order Theory of Successor (with Lawrence H. Landweber).- [26] The Complete Extensions of the Monadic Second Order Theory of Countable Ordinals (with Dirk Siefkes).- [28] Deterministic Automata and the Monadic Theory of Ordinals