Mathematical Logic and Its Applications 2020

The issue "Mathematical Logic and Its Applications 2020" contains articles related to the following three directions: Descriptive Set Theory (3 articles). Solutions for long-standing problems, including those of A. Tarski and H. Friedman, are presented. 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. Submissions are invited for the next issue "Mathematical Logic and Its Applications 2021

Partielle Isomorphie

Die Dissertation befasst sich mit dem Konzept der partiellen Isomorphie und erreicht mit Hilfe modelltheoretischer Beweismethoden Verallgemeinerungen der klassischen Klassifikationstheoreme von Ulm und Warfield. Weiter wird unter Annahme von V=L eine Klasse überabzählbarer partiell isomorpher Moduln konstruiert, deren Ulm-Kaplansky Invarianten vorgegeben werden können.The thesis deals with the concept of partial isomorphism and uses model-theoretic methods to achieve generalizations of the classical classification theorems by Ulm and Warfield. Further, assuming V=L, we construct a class of uncountable, partially isomorphic modules with prescribed Ulm-Kaplansky invariants