Elementy teorii mnogości
Elements of Set Theory

Author(s): Marek Nowak
Subject(s): Philosophy, Logic
Published by: Wydawnictwo Uniwersytetu Łódzkiego
Keywords: cardinal numbers;transfinite sequence;sets of ordinal numbers;natural numbers;binary relations;well-founded and non-well-founded sets;axiomatic;set theory
Summary/Abstract: The monograph contains the most important elements of the Zermelo-Fraenkel axiomatic set theory with the axiom of choice: axiomatics, definitions of basic concepts, theories of binary relations, partial ordering, equivalence, functions, ordinal numbers and cardinal numbers.It was created on the basis of lectures conducted over many years by the author for philosophy students at the University of Łódź. Therefore, it does not require a thorough mathematical background; it is enough to have some logical "skills" in theorem proving, or, indeed, a knowledge of such logical constants as Boolean functions and quantifiers. It can be used not only by mathematicians and mathematics students, but also by humanists wishing to consolidate their knowledge of sets, often used in various formalization procedures. The more so because some topics have a philosophical character, including discussions about the axiom of regularity and the concept of founding a set, equivalence relation, ordinal number or axiom of choice.

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