Implications

This non-implication, Form 321 \( \not \Rightarrow \) Form 255, 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: 8101, whose string of implications is:
    255 \(\Rightarrow\) 260 \(\Rightarrow\) 40 \(\Rightarrow\) 328

The conclusion Form 321 \( \not \Rightarrow \) Form 255 then follows.

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

Name Statement

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