Implications

This non-implication, Form 0 \( \not \Rightarrow \) Form 269, whose code is 6, is constructed around a proven non-implication as follows:

  • This non-implication was constructed without the use of this first code 2/1 implication.
  • A proven non-implication whose code is 5. In this case, it's Code 3: 1, Form 0 \( \not \Rightarrow \) Form 269 whose summary information is:
    Hypothesis Statement
    Form 0  \(0 = 0\).

    Conclusion Statement
    Form 269 <p> For every cardinal \(m\), there is a set \(A\) such that \(2^{|A|^2}\ge m\) and there is a choice function on the collection of 2-element subsets of \(A\). </p>

  • This non-implication was constructed without the use of this last code 2/1 implication

The conclusion Form 0 \( \not \Rightarrow \) Form 269 then follows.

Finally, the
List of models where hypothesis is true and the conclusion is false:

Name Statement

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