Tom IX | **The present state of investigations on the foundations of mathematics ** | INTRODUCTION
A. THEORY OF MATHEMATICAL NOTIONS
A1. The axiomatic method
A1a. Elementary and non-elementary HyuteniB of axionm
A1aa. General definitons
A1ab. The general theory of elementary systems
A1ac. The notion of categoricity and the theory of non-elementary systems
A1b. The axiomatic method applied to concrete mathematical theories
A1ba. The arithmetic of natural numbers
A1bb. The axiomatic theory of sets
A1bc. The axioms of the theory of real numbers
A2. Constructive trends in foundations of mathematics
A2a. The axiom of constructibility
A2b. The ramified theory of types
A2c. The computable analysis
A2d. The intuitionistic logic
General appreciation
B. THEORY OF MATHEMATICAL PROOFS
B1. The axiomatization of logic
B2. The decision problems
General appreciation of the present state of the decision problem
C. THE THEORY OF RECURSIVE FUNCTIONS AND THE ALGEBRAIC TREND
BIBLIOGRAPHY |