Implications

This non-implication, Form 250 \( \not \Rightarrow \) Form 127, whose code is 4, is constructed around a proven non-implication as follows:

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 7466, whose string of implications is:
    121 \(\Rightarrow\) 122 \(\Rightarrow\) 250
  • A proven non-implication whose code is 3. In this case, it's Code 3: 1013, Form 121 \( \not \Rightarrow \) Form 127 whose summary information is:
    Hypothesis Statement
    Form 121 <p> \(C(LO,<\aleph_{0})\): Every linearly ordered set of non-empty finite sets has a choice function. </p>

    Conclusion Statement
    Form 127 <p> An amorphous power of a compact \(T_2\) space, which as a set is well orderable, is well orderable. </p>

  • This non-implication was constructed without the use of this last code 2/1 implication

The conclusion Form 250 \( \not \Rightarrow \) Form 127 then follows.

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

Name Statement
\(\cal N24\) Hickman's Model I This model is a variation of \(\cal N2\)

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