EDB — 252

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E57

[252]Prerequisites:[23T],[026],[1Y0],[00S]. Let \(A\) be a non-empty set; we define \(B\) as the set that contains all the elements that are in all the elements of \(A\). Write a well-formed formula that defines \(B\), prove that \(B\) is indeed a set, and show that it is unique; for symmetry with the axiom [026] we will indicate it with

\[ B = \underline⋂ A\quad . \]

It is related to the usual notation by the relation

\[ \underline⋂ A = ⋂ _{x\in A} x \quad . \]

Solution 1

[254]

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  • formula, well-formed —
  • \( \underline \bigcap \)
  • formal set theory
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