Author(s): A. Kino, J. Myhill and R.E. Vesley (Eds.)
Series: Studies in Logic and the Foundations of Mathematics 60
Publisher: Elsevier Science
Year: 1970
Language: English
Pages: iii-viii, 1-516
Content:
Edited by
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
