TAILIEUCHUNG - STUDIES IN LOGIC AND THE FOUNDATIONS OF MATHEMATICS

This volume constitutes the Proceedings of the Third International Congress for Logic, Methodology and Philosophy of Science. The Congress was held at the Grand Hotel Krasnapolsky, Amsterdam, from August 25 to September 2, 1967, under the joint of the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science. The Congress took place in the Netherlands at the invitation of the Nederlandse Vereniging voor Logica en Wijsbegeerte der Exacte Wet enschap pen | nttovwn III UW J Il VAxaxnviAAM t HAU STUDIES IN LOGIC AND THE FOUNDATIONS OF MATHEMATICS Editors A. HEYTING Amsterdam A. MOSTOWSKI Warszawa A. ROBINSON New Haven p. SUPPES Stanford Advisory Editorial Board Y. BAR-HILLEL Jerusalem K. L. DE BOUVÈRE Santa Clara H. HERMES Freiburg . J. HI NT IKK A Helsinki J. c. SHEPHERDSON Bristol E. p. SPECKER Zurich NORTH-HOLLAND PUBLISHING COMPANY AMSTERDAM Volume 52 Pages iv-xiii 1-554 1968 Logic Methodology and Philosophy of Science III Edited by B. Van Rootselaar and . Staal ISBN 9780444534163 ASIN B000UDX0UO 1. Advisory Editorial Board Page iv 2. Edited by Page v 3. Copyright page Page vi 4. Preface Pages xi-xii The Editors 5. List of Donors Page xiii 6. Speech by Professor A. Heyting Pages 1-3 7. Speech by Professor A. Heyting Page 4 8. In Memoriam A. I. Malcev Pages 5-6 Yu. L. Ershov 9. Infinitary Properties of Models Generated from Indiscernibles Pages 9-21 . Chang 10. Two Complete Algebraic Theories of Logic Pages 23-29 W. Craig 11. Numbered Fields Pages 31-34 . Ershov 12. Models with Orderings Pages 35-62 . Keisler 13. Recursion Theory as a Branch of Model Theory Pages 63-86 R. Montague 14. Craig s Interpolation Theorem in Some Extended Systems of Logic Pages 87-103 A. Mostowski 15. Formalization Principle Pages 105-118 G. Takeuti 16. Autonomous Transfinite Progressions and the Extent of Predicative Mathematics Pages 121-135 S. Feferman 17. Constructive Functions in The Foundations of Intuttionistic Mathematics Pages 137-144 . Kleene 18. Functions Ordinals Species Pages 145-159 G. Kreisel 19. Formal Systems of Intuitionistic Analysis I Pages 161-178 J. Myhill 20. On Simple Type Theory with Extensionality Pages 179-184 K. Schutte 21. Constructive Reasoning Pages 185-199 . Tait 22. The Theory of Choice Sequences Pages 201-223 . Troelstra 23. Problems in the Theory of Programming Languages Pages 227-238 J 24. Computable and Uncomputable Elements of Syntax Pages 239-254 H. Hiz 25. On the Notion of a

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