Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 129, 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: 934, Form 163 \( \not \Rightarrow \) Form 84 whose summary information is:
    Hypothesis Statement
    Form 163 <p> Every non-well-orderable set has an infinite, Dedekind finite subset. </p>

    Conclusion Statement
    Form 84 <p> \(E(II,III)\) (<a href="/articles/Howard-Yorke-1989">Howard/Yorke [1989]</a>): \((\forall x)(x\) is \(T\)-finite  if and only if \(\cal P(x)\) is Dedekind finite). </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 136, whose string of implications is:
    129 \(\Rightarrow\) 4 \(\Rightarrow\) 9 \(\Rightarrow\) 84

The conclusion Form 163 \( \not \Rightarrow \) Form 129 then follows.

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

Name Statement

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