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Heyting'88 Summer School and Conference on Mathematical Logic, held September 13 - 23, 1988 in Chaika, Bulgaria, was honourably dedicated to Arend Heyting's 90th anniversary. It was organized by Sofia University "Kliment Ohridski" on the occasion of its centenary and by the Bulgarian Academy of Sciences, with sponsorship of the Association for Symbolic Logic. The Meeting gathered some 115 participants from 19 countries. The present volume consists of invited and selected papers. Included are all the invited lectures submitted for publication and the 14 selected contributions, chosen out of 56 submissions by the Selection Committee. The selection was made on the basis of reports of PC members, an average of 4 per sLlbmission. All the papers are concentrated on the topics of the Meeting: Recursion Theory, Modal and Non-classical Logics, Intuitionism and Constructivism, Related Applications to Computer and Other Sciences, Life and Work of Arend Heyting. I am pleased to thank all persons and institutions that contributed to the success of the Meeting: sponsors, Programme Committee members and additional referees, the members of the Organizing Committee, our secretaries K. Lozanova and L. Nikolova, as well as K. Angelov, V. Bozhichkova, A. Ditchev, D. Dobrev, N. Dimitrov, R. Draganova, G. Gargov, N. Georgieva, M. Janchev, P. Marinov, S. Nikolova, S. Radev, I. Soskov, A. Soskova and v. Sotirov, who helped in the organization, Plenum Press and at last but not least all participants in the Meeting and contributors to this volume.
List of contents
Heyting Session (Invited Papers).- On the Early History of Intuitionistic Logic.- Heyting and Intuitionistic Geometry.- Summer School (Invited Lectures).- Provability Logics for Relative Interpretability.- Constructive Mathematics and Computer-Assisted Reasoning Systems.- Markov's Constructive Mathematical Analysis: the Expextations and Results.- Normalization Theorems for the Intuitionistic Systems with Choice Principles.- Formalizing the Notion of Total Information.- Structural Rules and a Logical Hierarchy.- Semantics of Non-classical First Order Predicate Logics.- On the Computational Power of the Logic Programs.- Some Relations among Systems for Bounded Arithmetic.- A Survey of Intuitionistic Descriptive Set Theory.- Interpretability Logic.- Hierarchies of Provably Computable Functions.- Conference (Contributed Papers).- Sequent Calculus for Intuitionistic Linear Propositional Logic.- Order Isomorphisms - a Constructive Measure-Theoretic View.- 1-Generic Enumeration Degrees Below Oe'.- Remarks on Denjoy Sets.- Normal Modal Logic in Which the Heyting Proposotional Calculus Can be Embedded.- Lattices Adequate for Intutionistic Predicate Logic.- A Note on Boolean Modal Logic.- Completeness and Incompleteness in the Bimodal Base L(R,?R).- A Temporal Logic for Event Structures.- Completeness of Propositional Dynamic Logic with Infinite Repeating.- An Equivalence between Polinomial Constructivity of Markov's Principle and Equality P=NP.- Effective Enumerations of Abstract Structures.- Modal Characterization of the Classes of Finite and Infinite Quasi-Ordered Sets.- Least Fixed Points in Preassociative Combinatory Algebras.- Participants, Contributors and Programme Committee Members.
