Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 144, 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: 995, Form 163 \( \not \Rightarrow \) Form 125 whose summary information is:
    Hypothesis Statement
    Form 163 <p> Every non-well-orderable set has an infinite, Dedekind finite subset. </p>

    Conclusion Statement
    Form 125 <p> There does not exist an infinite, compact connected \(p\) space. (A \(p\) <em>space</em> is a \(T_2\) space in which the intersection of any well orderable family of open sets is open.) </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 9639, whose string of implications is:
    144 \(\Rightarrow\) 125

The conclusion Form 163 \( \not \Rightarrow \) Form 144 then follows.

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

Name Statement

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