Front Matter....Pages i-xiv Front Matter....Pages 1-1 Remarks Concerning Kurt Gödel’s Life and Work....Pages 3-7 Facets of Incompleteness....Pages 9-21 Godel’s Life and Work....Pages 23-36 Front Matter....Pages 37-37 Categorial Grammar and Lambda Calculus....Pages 39-60 A Constructive Morse Theory of Sets....Pages 61-79 Differentiation of Constructive Functions of a Real Variable and Relative Computability....Pages 81-106 A Completeness Theorem for Higher-Order Intuitionistic Logic: An Intuitionistic Proof....Pages 107-124 Reasoning in Trees....Pages 125-135 Non-Deterministic Program Schemata and Their Relation to Dynamic Logic....Pages 137-147 The Parallel Evaluation of Functional Programs....Pages 149-165 Logic Approximating Sequences of Sets....Pages 167-186 Intuitionistic Formal Spaces — A First Communication....Pages 187-204 On the Logic of Small Changes in Theories II....Pages 205-211 On ‘Logical Relations’ in Program Semantics....Pages 213-229 Front Matter....Pages 231-231 Search Computability and Computability with Numberings Are Equivalent in the Case of Finite Set of Objects....Pages 233-242 Cut-Elimination Theorem for Higher-Order Classical Logic: An Intuitionistic Proof....Pages 243-251 Modal Environment for Boolean Speculations....Pages 253-263 Distributive Spaces....Pages 265-272 Approximating the Projective Model....Pages 273-282 Projection Complete Graph Problems Corresponding to a Branching-Program-Based Characterization of the Complexity Classes NC 1 , L and NL ....Pages 283-292 Front Matter....Pages 231-231 Constructive Theories with Abstract Data Types for Program Synthesis....Pages 293-302 A First Order Logic for Logic Programming....Pages 303-314 The Relational Semantics for Branched Quantifiers....Pages 315-322 Propositional Dynamic Logic in Two- and More Dimensions....Pages 323-329 On a Nonconstructive Type Theory and Program Derivation....Pages 331-340 Prime Computability on Partial Structures....Pages 341-350 Complexity Bounded Martin-Löf Tests....Pages 351-359 Back Matter....Pages 361-371 The Summer School and Conference on Mathematical Logic and its Applications, September 24 - October 4, 1986, Druzhba, Bulgaria, was honourably dedicated to the 80-th anniversary of Kurt Godel (1906 - 1978), one of the greatest scientists of this (and not only of this) century. The main topics of the Meeting were: Logic and the Foundation of Mathematics; Logic and Computer Science; Logic, Philosophy, and the Study of Language; Kurt Godel's life and deed. The scientific program comprised 5 kinds of activities, namely: a) a Godel Session with 3 invited lecturers b) a Summer School with 17 invited lecturers c) a Conference with 13 contributed talks d) Seminar talks (one invited and 12 with no preliminary selection) e) three discussions The present volume reflects an essential part of this program, namely 14 of the invited lectures and all of the contributed talks. Not presented in the volltme remai ned si x of the i nvi ted lecturers who di d not submi t texts: Yu. Ershov - The Language of!:-expressions and its Semantics; S. Goncharov - Mathematical Foundations of Semantic Programming; Y. Moschovakis - Foundations of the Theory of Algorithms; N. Nagornyj - Is Realizability of Propositional Formulae a GBdelean Property; N. Shanin - Some Approaches to Finitization of Mathematical Analysis; V. Uspensky - Algorithms and Randomness - joint with A.N
