Gödel 96: Logical Foundations of Mathematics, Computer Science, and Physics
Petr Hájek (Editor)
This volume, the sixth publication in the Lecture Notes in Logic series, collects the proceedings of the conference ‘Logical Foundations of Mathematics, Computer Science, and Physics – Kurt Gödel’s Legacy’, held in Brno, Czech Republic, on the 90th anniversary of Gödel’s birth. The broad range of speakers who participated in this event affirms the continuing importance of Gödel’s work in logic, physics, and the philosophy and foundations of mathematics and computer science. The papers in this volume range over all these topics and contribute to our present understanding of them.
Table of Contents
Part I. Invited Papers
- Gödel’s program for new axioms: Why, where, how and what?
- Infinite-valued Gödel Logics with 0-1-Projections and Relativizations.
- Contributions of K. Gödel to Relativity and Cosmology.
- Kurt Gödel and the constructive Mathematics of A.A. Markov.
Boris A. Kushner
- Hao Wang as Philosopher.
- A bottom-up approach to foundations of mathematics.
- K-graph Machines: generalizing Turing’s machines and arguments.
Wilfried Sieg and John Byrnes
- Forcing on Bounded Arithmetic.
Gaisi Takeuti and Masahiro Yasumoto
- Uniform Interpolation and Layered Bisimulation.
Part II. Contributed Papers
- Gödel’s Ontological Proof Revisited.
C. Anthony Anderson and Michael Gettings
- A Uniform Theorem Proving Tableau Method for Modal Logic.
- Decidability of the $\exists^*\forall^*$-Class in the Membership Theory NWL.
Dorella Bellè and Franco Parlamento
- A Logical Approach to Comlexity Bounds for Sbutype Inequalities.
- How to characterize provably total functions.
Benjamin Blankertz and Andreas Weiermann
- Completeness has to be restricted: Gödel’s interpretation of the parameter t.
- A Bounded Arithmetic Theory for Constant Depth Threshold Circuits.
- Information content and computational complexity of recursive sets.
- Kurt Gödel and the Consistency of R##.
Robert K. Meyer
- Best possible answer is computable for fuzzy SLD-resolution.
- The finite stages of inductive definitions.
Robert F. Stärk
- Gödel and the Theory of Everything.
- Replacement $\not\to$ Collection.
Andrezej M. Zarach