Implications

This non-implication, Form 321 \( \not \Rightarrow \) Form 66, whose code is 6, 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 5. In this case, it's Code 3: 640, Form 321 \( \not \Rightarrow \) Form 328 whose summary information is:
    Hypothesis Statement
    Form 321 <p> There does not exist an ordinal \(\alpha\) such that \(\aleph_{\alpha}\) is weakly compact and \(\aleph_{\alpha+1}\) is measurable. </p>

    Conclusion Statement
    Form 328 <p> \(MC(WO,\infty)\): For  every well ordered set \(X\) such that for all \(x\in X\), \(|x|\ge 1\), there is a function \(f\) such that and for every \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\). (See <a href="/form-classes/howard-rubin-67">Form 67</a>.) </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 4895, whose string of implications is:
    66 \(\Rightarrow\) 67 \(\Rightarrow\) 328

The conclusion Form 321 \( \not \Rightarrow \) Form 66 then follows.

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

Name Statement

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