Implications

This non-implication, Form 307 \( \not \Rightarrow \) Form 381, whose code is 6, is constructed around a proven non-implication as follows:
Note: This non-implication is actually a code 4, as this non-implication satisfies the transferability criterion. Click Transfer details for all the details)

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 6895, whose string of implications is:
    91 \(\Rightarrow\) 305 \(\Rightarrow\) 307
  • A proven non-implication whose code is 5. In this case, it's Code 3: 241, Form 91 \( \not \Rightarrow \) Form 382 whose summary information is:
    Hypothesis Statement
    Form 91 <p> \(PW\):  The power set of a well ordered set can be well ordered. </p>

    Conclusion Statement
    Form 382 <p> <strong>DUMN</strong>:  The disjoint union of metrizable spaces is normal. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 10026, whose string of implications is:
    381 \(\Rightarrow\) 382

The conclusion Form 307 \( \not \Rightarrow \) Form 381 then follows.

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

Name Statement
\(\cal N53\) Good/Tree/Watson Model I Let \(A=\bigcup \{Q_n:\ n\in\omega\}\), where \(Q_n=\{a_{n,q}:q\in \Bbb{Q}\}\)

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