EDB — 241

Zermelo–Fraenkel axioms[241]

We now briefly discuss the axioms of Zermelo–Fraenkel set theory.

1. Axiom of extensionality, already seen above in [1Y8]↺↻.

2. [014]↺↻

3. [1Y3]↺↻

4. [026]↺↻

5. [1Y1]↺↻

6. Axiom of infinity (see [243]↺↻)

7. [1Y0]↺↻

8. Axiom of good foundation, or regularity (see [01R]↺↻)

9. Axiom of replacement

(We have omitted the definitions of ”Axiom of replacement”; you can find it in Chap.1 Sec.16 in  [ 3 ] or Chap. 1 in [ 14 ] ).

A further axiom is the Axiom of Choice; it will be discussed in Sec. [23R]↺↻.

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[23W]↺↻

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[23T]↺↻

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[252]↺↻

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[247]↺↻

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[028]↺↻

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[248]↺↻

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[1W4]↺↻

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[023]↺↻

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[1Y9]↺↻

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[01N]↺↻

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[1YD]↺↻

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[029]↺↻

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[01R]↺↻

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[01W]↺↻

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[01Y]↺↻

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[020]↺↻

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[022]↺↻

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[024]↺↻