Logic II, 7.5 ECTS
Second levelFacts
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The course covers: • Fundamentals and set theory: The Zermelo-Fraenkel axioms of set theory, elementary theory for cardinals and ordinals. Equivalent formulations of the axiom of choice and its applications in analysis and algebra. • Structures and models: Isomorphisms and embeddings, complete theories, elementary equivalence and elementary embedding, Löwenheim-Skolem’s theorems, categoricality, applications on algebraic theories and non-standard analysis. • Computability and incompleteness: Models of computation, classes of computable functions, decidable and irreversible problems, Gödel coding and Gödel’s incompleteness theorem.
Area of interests: Science and Mathematics
Science and mathematics help us understand how the world around us is connected – from the origin and structure of the universe, to the development and function of humanity and all other organisms on earth. Scientific knowledge makes it possible to critically examine the credibility of information in different areas of everyday life, society, and the media. As a scientist or mathematician, you will be attractive on a large job market that covers all parts of society and includes everything from pure technology companies to environment and healthcare, as well as research.
Subject
Mathematics
As a mathematical theory always implies that certain conclusions hold under certain given conditions, it can in principle say nothing about the physical reality. None the less mathematics has become an indispensable tool for a large number of subjects like astronomy, physics, chemistry, statistics and the technical sciences and in later times also for economy, biology, various social sciences and computor science. The role of mathematics in the applied sciences is both to supply notions for exact and adequate formulations of empirical laws but also from these laws to derive consequences, which can be used to find better models of the reality one has to describe. These tasks have lately become more important. Mathematics is in continual progress by intensive international research, new theories are created and already existing theories are simplified and augmented.