Cover

Half-title

Series information

Title page

Copyright information

Preface

The Topics

Logic in Israel

The Participants

The Hosting Institutions

Financial Support

Teamwork

Plenary sessions

Tutorials

Plenary addresses

Special sessions

Finite model theory and computer science

Model theory

Set theory

Recursion theory

Proof theory

Non-monotonic and non-classical logic

Organizing and program committees

Program Committee

Special Session Advisors

Organizing Committee

Local Organizing Staff

Technical Support

Table of contents

The Number of Path-Components of a Compact Subset of R[sup(n)]

0. Introduction

1. Path-components

2. Statement of theorems

3. Descriptive set theory and equivalence relations, I: Theorems of Silver and Burgess

4. Path-components in compact subsets of R[sup(3)]

5. Descriptive set theory and equivalence relations, II: Stern's Theorem

6. Theta-curves

7. Path-components in compact subsets of R[sup(2)]

References

Intervals Without Critical Triples

1 Introduction

2 Definitions and Examples

3 The requirements N[sub(1)]

4 Lower Cones

4.1 Nonbounding

4.2 Splitting

4.3 Nonlow nonbounding

5 The requirement P[sub())]

6 Upper Cones

6.1 Upward nonbounding

6.2 Upward and downward nonbounding

6.3 P[sub(upharpoonleft,\S)] and lowness requirements

References

Beyond Godel's Theorem: Turing Nonrigidity Revisited

References

Types and Indiscernibles in Finite Models

1 Introduction

2 Finite Variable Logics

3 Finitary Lowenheim-Skolem Properties

4 Trees

5 Indiscernibles

References

Model Theory of Modules

References

Noninterpretability of Infinite Linear Orders

1 Squares

2 Applications in recursion theory

References

Combinatorial Principles from Adding Cohen Reals

1 Introduction

2 The combinatorial principles

3 Consistency of the principles in the Cohen model

4 Applications

References

Extensions of Models of PV

Introduction

1 Preliminaries

2 An ultrapower

3 A compactness argument

4 A Boolean-valued extension

5 A construction of a counter-example function

References

Convergence Laws for Random Graphs

1 Background

2 Recursive Logics and Infinitary Logics

3 Random Graphs

4 Future Directions

References

V=L and Maximize

1 Naturalism

2 Maximize and Unify

3 Why V=L is restrictive

4 What goes wrong

References

Towards a Categorical Foundation of Mathematics

1. Introduction

2. The universe and the language

3. Abstract sets

4. Functions, categories and isomorphisms

5. A revision of category theory

6. 2-dimensional categories

7. Higher dimensional categories

8. Dependent types

9. Formal systems

10. Equivalence in FOLDS

11. In variance under L-equivalence

References

Strongly Minimal Sets and Geometry

1 Strongly minimal sets and pregeometries

2 Families of plane curves

3 Algebraic structure

4 Zariski geometries

5 The Mordell-Lang conjecture for function fields

References

Computationally-Sound Proofs

1 Introduction

2 Prior Notions and New Goals

2.1 Prior Notions of a Proof

2.2 Complexity, Polynomial Time and Classical Proofs

2.3 New Goals For Efficient Proofs

3 Computationally-Sound Proofs

3.1 CS Proofs With A Random Oracle

3.2 CS Proofs with a Random String

3.3 Deterministic CS Proofs

4 Certified Computation

5 Final Remarks

6 Acknowledgments

References

Lambek Calculus and Formal Languages

Introduction

1 Preliminaries

2 Lambek grammars recognize context-free languages

3 L-completeness of the Lambek calculus

References

Zil'ber's Trichotomy and o-minimal Structures

References

The Higher Infinite in Proof Theory

1 Introduction

2 Observations on ordinal analyses

3 Large cardinals and ordinal representation systems I

3.1 A brief history of ordinal representation systems up till the early 1980s

3.2 Ordinal functions based on a weakly inaccessible cardinal

3.3 Ordinal functions based on a weakly Mahlo cardinal

3.4 Ordinal functions based on a weakly compact cardinal

4 Recursively large ordinals and ordinal representation systems

5 Large Cardinals and ordinal representation systems II

6 Large sets in constructive set theory

6.1 The System CZF

6.2 Inaccessibility

6.3 Mahloness

6.4 Weak compactness

References

There May Be No Nowhere Dense Ultrafilter

0 Introduction

1 The basic forcing

2 NWD ultrafilters

3 The consistency proof

References

Towards Recursive Model Theory

1 Introduction

2 Preliminaries

2.1 Recursive models

2.2 Tennenbaum's Theorem and generalizations

2.3 Monotone formulas

3 Classical Theorems in Recursive Models

4 Failure of Lyndon's Lemma

4.1 Positive preservation and pebble games

4.2 Rotated grids

4.3 Monotone separation of rotated grids

5 Conclusion

Acknowledgment

References

Accessible Segments of the Fast Growing Hierarchy

1 Introduction

2 Ordinal Presentations and Scales

3 Recognition by Descent Functionals

4 Recognition by Minimum Scales

References

Author Index