Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 114, 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: 979, Form 163 \( \not \Rightarrow \) Form 118 whose summary information is:
    Hypothesis Statement
    Form 163 <p> Every non-well-orderable set has an infinite, Dedekind finite subset. </p>

    Conclusion Statement
    Form 118 <p> Every linearly orderable topological space is normal.  <a href="/books/28">Birkhoff [1967]</a>, p 241. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 6538, whose string of implications is:
    114 \(\Rightarrow\) 90 \(\Rightarrow\) 118

The conclusion Form 163 \( \not \Rightarrow \) Form 114 then follows.

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

Name Statement

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