Implications

This non-implication, Form 118 \( \not \Rightarrow \) Form 301, 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: 1269, Form 118 \( \not \Rightarrow \) Form 300 whose summary information is:
    Hypothesis Statement
    Form 118 <p> Every linearly orderable topological space is normal.  <a href="/books/28">Birkhoff [1967]</a>, p 241. </p>

    Conclusion Statement
    Form 300 <p> Any continuous surjection between extremally disconnected compact Hausdorff spaces has an irreducible restriction to a closed subset of its domain. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 9606, whose string of implications is:
    301 \(\Rightarrow\) 300

The conclusion Form 118 \( \not \Rightarrow \) Form 301 then follows.

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

Name Statement
\(\cal M1\) Cohen's original model Add a denumerable number of generic reals (subsets of \(\omega\)), \(a_1\), \(a_2\), \(\cdots\), along with the set \(b\) containing them

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