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  3. Sets and Transfinite Algebra
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  • Publisher:
    Cambridge University Press
    Publication date:
    02 April 2026
    09 April 2026
    ISBN:
    9781009737883
    9781009737845
    9781009737876
    DOI:
    https://doi.org/10.1017/9781009737883
    Dimensions:
    (229 x 152 mm)
    Weight & Pages:
    0.469kg, 218 Pages
    Dimensions:
    (229 x 152 mm)
    Weight & Pages:
    0.323kg, 218 Pages
    • Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Algebra
    Series:
    London Mathematical Society Student Texts (110)
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    Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Algebra
    Series:
    London Mathematical Society Student Texts (110)
    Information

    Book description

    This two-part book offers a rigorous yet accessible exploration of set theory and transfinite algebra, with a particular emphasis on the axiom of choice and its applications. Part I presents an informal axiomatic introduction to the foundations of set theory, including a detailed treatment of the axiom of choice and its equivalents, suitable for advanced undergraduates. Part II, aimed at graduate students and professional mathematicians, treats selected topics in transfinite algebra where the axiom of choice, in one form or another, is useful or even indispensable. The text features self-contained chapters for flexible use, and includes material rarely found in the literature, such as Tarski's work on complete lattices, Hamel's solution to Cauchy's functional equation, and Artin's resolution of Hilbert's 17th problem. Over 140 exercises, with full solutions provided in the Appendix, support active engagement and deeper understanding, making this a valuable resource for both independent study and course preparation.

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