Preface

Benedikt Lowe, Florian Rudolph

1-4

The formal sciences

their scope, their foundations, and their unity

Benedikt Lowe

5-11

Slow versus fast growing

Andreas Weiermann

13-29

Applications of elementary submodels in general topology

Stefan Geschke

31-41

The history of applied mathematics and the history of society

Michael Stolz

43-57

Leibniz's rigorous foundation of infinitesimal geometry by means of Riemannian sums

Eberhard Knobloch

59-73

A term of length 4 523 659 424 929

A. D. Mathias

75-86

Large numbers, Knuth's arrow notation, and Ramsey theory

Hans-Jürgen Prömel

87-105

Tarski's fixed-point theorem and lambda calculi with monotone inductive types

Ralph Matthes

107-129

Games in the semantics of programming languages

an elementary introduction

Jan Jürjens

131-158

The incan quipus

Antje Christensen

159-172

Model checking techniqes for the analysis of reactive systems

Stephan Merz

173-201

Comparing approaches to resolution based higher-order theorem proving

Christoph Benzmüller

203-335

Mathematical proof theory in the light of ordinal analysis

Reinhard Kahle

237-255

Concepts and aims of functional interpretations

towards a functional interpretation of constructive set theory

Wolfgang Burr

257-274

The category of inner models

Peter Koepke

275-303