Content: Intro
Foreword
Preface
Contents
Contributors
Introduction: Solomon Feferman's Autobiography from 1928 to 1981 and Extensions
Part A: An Intellectual (Mostly) Autobiography
Part B: Solomon Feferman's CV
Part C: Active Projects of 2016
C1. Logic, Mathematics and Conceptual Structuralism
C2. Foundations of Explicit Mathematics
C3. Many-sorted First-order Model Theory as a Conceptual Framework for Biological and Other Complex Dynamical Systems
C4. Semi-intuitionistic Theories of Sets
Solomon Feferman Publications
Part I Mathematical Logic. From Choosing Elements to Choosing Concepts: The Evolution of Feferman's Work in Model Theory1 Logic When Feferman Entered the Field
2 The Feferman-Vaught Theorem
3 Applications of Interpolation Theorems
4 The Concept of Model Theory
References
Feferman on Computability
1 Inductive Schemata and Recursively Continuous Functionals
2 A New Approach to Abstract Data Types, Parts I and II
3 Computation on ADTs: The Extensional Approach
4 About and Around Computing over the Reals
5 Conclusion
References
On the Computability of the Fan Functional
1 Introduction
2 Background. 7 Defining the Bachmann Hierarchy by Functionals of Higher TypeReferences
The Interpretation Existence Lemma
1 Introduction
1.1 Historical Remarks
1.2 Interpretation Existence Without Induction
1.3 What Is in the Paper?
1.4 What Is Not in the Paper?
1.5 Prerequisites
2 Basic Notions and Facts
2.1 Theories
2.2 Translations and Interpretations
2.3 Provability, Arithmetization, Complexity
2.4 Sequential Theories
2.5 Shortening Cuts
3 The Interpretation Existence Lemma
3.1 Auxiliary Theories
3.2 The Theorem and Its Proof
3.3 Extending the Target Theory to a Sequential Theory. 3.4 An Equivalent of sf(V)3.5 Treatment of Numerals
3.6 The Collapse
3.7 The Second Incompleteness Theorem
4 Characterization Theorems and The World of
4.1 ast, n
4.2 ast, ast
4.3 ast, infty
5 Examples
5.1 End-Extensions
5.2 Properties of Degree Structures
5.3 The Interpretability of Inconsistency
References
Tiered Arithmetics
1 Introduction
2 Representing Algorithms in Linear Two-Sorted Arithmetic
2.1 The Term Systems T(
) and LT(
)
2.2 The Theories A(
) and LA(
)
2.3 Treesort
2.4 Treesort in LA(
)+ Flatten
3 Transfinitely Iterated Tiering.