Axiomatic Set Theory

Axiomatic Set Theory (Axiomatic Set Theory) is one of the main branches of mathematical logic. It is the study of reconstructing (naive) set theory using axiomatic methods, as well as the metamathematics of set theory and the study of new axioms of set theory. This book is the result of the author's many years of research on set theory. It has 13 chapters in total, including the following and part of the content: sets, relations, functions, order, natural numbers, finite, countable and uncountable sets, cardinal numbers, ordinal numbers, Aleph, axiom of choice, real number sets, filters and ultrafiltration, large cardinal numbers, basic axioms and anti-basic axioms, various systems of axiomatic set theory, etc. This book can be used as a textbook for axiomatic set theory courses for senior undergraduates and graduate students majoring in mathematics, and can also be used as a reference book for teachers of related majors in colleges and universities.