Implications

This non-implication, Form 0 \( \not \Rightarrow \) Form 259, whose code is 4, 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 3. In this case, it's Code 3: 75, Form 0 \( \not \Rightarrow \) Form 208 whose summary information is:
    Hypothesis Statement
    Form 0  \(0 = 0\).

    Conclusion Statement
    Form 208 <p> For all ordinals \(\alpha\), \(\aleph_{\alpha+1}\le 2^{\aleph_\alpha}\). </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 4165, whose string of implications is:
    259 \(\Rightarrow\) 51 \(\Rightarrow\) 208

The conclusion Form 0 \( \not \Rightarrow \) Form 259 then follows.

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

Name Statement

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