Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 3, 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: 903, Form 163 \( \not \Rightarrow \) Form 53 whose summary information is:
    Hypothesis Statement
    Form 163 <p> Every non-well-orderable set has an infinite, Dedekind finite subset. </p>

    Conclusion Statement
    Form 53 <p> For all infinite cardinals \(m\), \(m^2\le 2^m\).  <a href="/articles/Mathias-1979">Mathias [1979]</a>, prob 1336. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 10161, whose string of implications is:
    3 \(\Rightarrow\) 53

The conclusion Form 163 \( \not \Rightarrow \) Form 3 then follows.

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

Name Statement

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