Implications

This non-implication, Form 119 \( \not \Rightarrow \) Form 133, 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: 6740, whose string of implications is:
    90 \(\Rightarrow\) 118 \(\Rightarrow\) 119
  • A proven non-implication whose code is 5. In this case, it's Code 3: 190, Form 90 \( \not \Rightarrow \) Form 221 whose summary information is:
    Hypothesis Statement
    Form 90 <p> \(LW\):  Every linearly ordered set can be well ordered. <a href="/books/8">Jech [1973b]</a>, p 133. </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: 4847, whose string of implications is:
    133 \(\Rightarrow\) 63 \(\Rightarrow\) 221

The conclusion Form 119 \( \not \Rightarrow \) Form 133 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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