Implications

This non-implication, Form 190 \( \not \Rightarrow \) Form 63, whose code is 6, 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: 7695, whose string of implications is:
    191 \(\Rightarrow\) 189 \(\Rightarrow\) 190
  • A proven non-implication whose code is 5. In this case, it's Code 3: 495, Form 191 \( \not \Rightarrow \) Form 221 whose summary information is:
    Hypothesis Statement
    Form 191 <p> \(SVC\): There is a set \(S\) such that for every set \(a\), there is an ordinal \(\alpha\) and a function from \(S\times\alpha\) onto \(a\). </p>

    Conclusion Statement
    Form 221 <p> For all infinite \(X\), there is a non-principal measure on \(\cal P(X)\). </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 10226, whose string of implications is:
    63 \(\Rightarrow\) 221

The conclusion Form 190 \( \not \Rightarrow \) Form 63 then follows.

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

Name Statement
\(\cal N51\) Weglorz/Brunner Model Let \(A\) be denumerable and \(\cal G\)be the group of all permutations of \(A\)

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