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  1. Zermelo–Fraenkel set theory
    • According to 2 sources
    In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.

    Zermelo–Fraenkel set theor…

    en.wikipedia.org
    ZFC is the acronym for Zermelo–Fraenkel set theory with the axiom of choice, formulated in first-order logic. ZFC is the basic axiom system for modern (2000) set theory, regarded both as a field of mathematical research and as a foundation for ongoing mathematics (cf. also Axiomatic set theory).

    ZFC - Encyclopedia of Math…

    encyclopediaofmath.org
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    What does ZFC stand for?
    Zermelo–Fraenkel set theory with the axiom of choice ZFC is the acronym for Zermelo–Fraenkel set theory with the axiom of choice, formulated in first-order logic. ZFC is the basic axiom system for modern (2000) set theory, regarded both as a field of mathematical research and as a foundation for ongoing mathematics (cf. also Axiomatic set theory).

    ZFC - Encyclopedia of Mathematics

    encyclopediaofmath.org
    What does ZF stand for in Zermelo-Fraenkel set theory?
    Zermelo–Fraenkel set theory with the axiom of choice included is abbreviated ZFC, where C stands for "choice", and ZF refers to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded.

    Zermelo–Fraenkel set theory - Wikipedia

    en.wikipedia.org
    What is the difference between axiomatic set theory and ZFC?
    Much of the power of ZFC, including the axiom of regularity and the axiom schema of replacement, is included primarily to facilitate the study of the set theory itself. On the other hand, among axiomatic set theories, ZFC is comparatively weak. Unlike New Foundations, ZFC does not admit the existence of a universal set.

    Zermelo–Fraenkel set theory - Wikipedia

    en.wikipedia.org
    Does ZFC admit the existence of a universal set?
    Unlike New Foundations, ZFC does not admit the existence of a universal set. Hence the universe of sets under ZFC is not closed under the elementary operations of the algebra of sets. Unlike von Neumann–Bernays–Gödel set theory (NBG) and Morse–Kelley set theory (MK), ZFC does not admit the existence of proper classes.

    Zermelo–Fraenkel set theory - Wikipedia

    en.wikipedia.org
    What is ZFC theory?
    Formally, ZFC is a one-sorted theory in first-order logic. The equality symbol can be treated as either a primitive logical symbol or a high-level abbreviation for having exactly the same elements. The former approach is the most common.

    Zermelo–Fraenkel set theory - Wikipedia

    en.wikipedia.org
    Is ZFC a strong axiom?
    In particular, most of modern mathematics can be proven in weaker axiomatic systems like the Peano axioms, and all of it can be carried out in ZC: Zermelo set theory with the axiom of choice (Zermelo theory is obtained from dropping the axiom of replacement). Thus, in some sense, ZFC is "too strong" for the sake of making set theory easier.

    ZFC | Brilliant Math & Science Wiki

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  3. Stanford Encyclopedia of Philosophy
    https://plato.stanford.edu › entries › set-theory › ZF.html

    Zermelo-Fraenkel Set Theory (ZF) - Stanford Encyclopedia of …

  4. PDF files of zfc theory
  5. Brilliant
    https://brilliant.org › wiki › zfc

    ZFC | Brilliant Math & Science Wiki

    ZFC, or Zermelo-Fraenkel set theory, is an axiomatic system used to formally define set theory (and thus mathematics in general). Specifically, ZFC is a collection of approximately 9 axioms (depending on convention and precise …

    Tags:
    The Axioms of Set Theory
    Zfc Set Theory
    Model of Zfc
    Understanding Zfc
  6. Wolfram MathWorld
    https://mathworld.wolfram.com › Zermelo-FraenkelAxioms.html

    Zermelo-Fraenkel Axioms -- from Wolfram MathWorld

    Tags:
    The Axioms of Set Theory
    Zermelo–Fraenkel set theory
  7. UCB Mathematics
    https://math.berkeley.edu › ~marks › notes
    [PDF]

    Set Theory - University of California, Berkeley

  9. Department of Mathematics | The University of Chicago
    https://math.uchicago.edu › ~may › VIGRE › REUPapers › Lian.pdf
    [PDF]

    Contents FUNDAMENTALS OF ZERMELO-FRAENKEL S

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    The Axioms of Set Theory
    Axioms of Zf
    Ernst Zermelo Abraham Fraenkel
  10. Encyclopedia of Mathematics
    https://encyclopediaofmath.org › wiki › ZFC

    ZFC - Encyclopedia of Mathematics

    Tags:
    Zfc Set Theory
    Zermelo–Fraenkel set theory
    Axiom of Choice Zfc
    Model of Zfc
  11. ETH Zurich
    https://people.math.ethz.ch › ~halorenz › LogikGT
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    Chapter 13 The Axioms of Set Theory ZFC - ETH Z

    Tags:
    The Axioms of Set Theory
    Zfc Set Theory
    Zfc Theory Axioms
  12. uh.edu
    https://www.math.uh.edu › ~klaus › discrete_math_zf.pdf
    [PDF]

    The Zermelo Fraenkel Axioms of Set Theory - UH

  13. Stanford Encyclopedia of Philosophy
    https://plato.stanford.edu › entries › set-theory-constructive

    Set Theory: Constructive and Intuitionistic ZF

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