The issue "Mathematical Logic and Its Applications 2020" contains articles related to the following three directions:
I. Descriptive Set Theory (3 articles). Solutions for long-standing problems, including those of A. Tarski and H. Friedman, are presented.
II. Exact combinatorial optimization algorithms, in which the complexity relative to the source data is characterized by a low, or even first degree, polynomial (1 article).
III. Applications of mathematical logic and the theory of algorithms (2 articles). The first article deals with the Jacobian and M. Kontsevich's conjectures, and algorithmic undecidability; for these purposes, non-standard analysis is used. The second article provides a quantitative description of the balance and adaptive resource of a human.
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Table of Contents
Models of Set Theory in which NonconstructibleReals First Appear at a Given Projective Level
On the Δ 1 n Problem of Harvey Friedman
On the 'Definability of Definable'Problem of Alfred Tarski
Linear Time Additively Exact Algorithm for Transformation of Chain-Cycle Graphs for Arbitrary Costs of Deletions and Insertions
Nonstandard Analysis, Deformation Quantization and Some Logical Aspects of (Non) Commutative Algebraic Geometry
Physiological Balance of the Body: Theory, Algorithms, and Results