Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo N.Y. 1968

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Page iii

Copyright page
Page iv

Introduction
Pages vii-viii
Akiko Kino, John Myhill, Richard Vesley

Section A New Directions
Page 1

The Ultra-Intuitionistic Criticism and the Antitraditional Program for Foundations of Mathematics Original Research Article
Pages 3-45
A.S. Yessenin-Volpin

Computable Analysis and Differential Equations Original Research Article
Pages 47-52
Oliver Aberth

Mathematics as a Numerical Language Original Research Article
Pages 53-71
Errett Bishop

On the Notion of Randomness Original Research Article
Pages 73-78
Per Martin-Löf

Abstract Quantification Theory Original Research Article
Pages 79-91
Raymond M. Smullyan

Section B Traditional Intuitionism
Page 93

Recent Progress in Intuitionistic Analysis Original Research Article
Pages 95-100
A. Heyting

A Theory of Constructions Equivalent to Arithmetic Original Research Article
Pages 101-120
Nicolas D. Goodman

Church's Thesis: A Kind of Reducibility Axiom for Constructive Mathematics Original Research Article
Pages 121-150
G. Kreisel

Formal Systems of Intuitionistic Analysis II: The Theory of Species Original Research Article
Pages 151-162
John Myhill

Projections of Lawless Sequences Original Research Article
Pages 163-186
D. van Dalen, A.S. Troelstra

On Subjective Mathematical Assertions Original Research Article
Pages 187-196
B. van Rootselaar

A Palatable Substitute for Kripke's Schema Original Research Article
Pages 197-207
R.E. Vesley

Section C Classical Interpretations of Intuitionism
Page 209

A Characterization of the Intuitionistic Propositional Calculus Original Research Article
Pages 211-217
D.H.J. de Jongh

Intuitionistic Model Theory and the Cohen Independence Proofs Original Research Article
Pages 219-226
Melvin Fitting

An Abstract Notion of Realizability for Which Intuitionistic Predicate Calculus is Complete Original Research Article
Pages 227-234
H. Läuchli

Extending the Topological Interpretation to Intuitionistic Analysis, II Original Research Article
Pages 235-255
Dana Scott

Section D Proof Theory of Intuitionism
Page 257

Some Results for Intuitionistic Logic with Second Order Quantification Rules Original Research Article
Pages 259-269
Dag Prawitz

On Cut Elimination in Intuitionistic Systems of Analysis Original Research Article
Pages 271-285
B. Scarpellini

Section E Proof-Theoretic Ordinals
Page 287

Hereditarily Replete Functionals Over the Ordinals Original Research Article
Pages 289-301
Solomon Feferman

Formal Theories for Transfinite Iterations of Generalized Inductive Definitions and Some Subsystems of Analysis Original Research Article
Pages 303-326
Solomon Feferman

Brouwer's Bar Theorem and a System of Ordinal Notations Original Research Article
Pages 327-338
Harvey Gerber

Regular Ordinals and Normal Forms Original Research Article
Pages 339-361
David Isles

Formalization of the Theory of Ordinal Diagrams of Infinite Order Original Research Article
Pages 363-376
Akiko Kino

On the Relationship Between Takeuti's Ordinal Diagrams O(n) and SchГјtte's System of Ordinal Notations ОЈ(n) Original Research Article
Pages 377-405
Hilbert Levitz

Section F Proof Theory
Page 407

On the Original Gentzen Consistency Proof for Number Theory Original Research Article
Pages 409-417
Paul Bernays

Herbrand-Style Consistency Proofs Original Research Article
Pages 419-433
Burton Dreben, John Denton

Iterated Inductive Definitions and ОЈ21-AC Original Research Article
Pages 435-442
Harvey Friedman

Assignment of Ordinals to Terms for Primitive Recursive Functionals of Finite Type Original Research Article
Pages 443-458
W.A. Howard

On a Number Theoretic Choice Schema and its Relation to Induction Original Research Article
Pages 459-473
Charles Parsons

Applications of the Cut Elimination Theorem to Some Subsystems of Classical Analysis Original Research Article
Pages 475-488
W.W. Tait

Principles of Proof and Ordinals Implicit in Given Concepts Original Research Article
Pages 489-516
G. Kreisel