Implications

This non-implication, Form 366 \( \not \Rightarrow \) Form 52, 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: 6583, whose string of implications is:
    90 \(\Rightarrow\) 91 \(\Rightarrow\) 79 \(\Rightarrow\) 367 \(\Rightarrow\) 366
  • 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: 9948, whose string of implications is:
    52 \(\Rightarrow\) 221

The conclusion Form 366 \( \not \Rightarrow \) Form 52 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 \(A\)

Edit | Back