Implications

This non-implication, Form 125 \( \not \Rightarrow \) Form 345, whose code is 4, 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: 9639, whose string of implications is:
    144 \(\Rightarrow\) 125
  • A proven non-implication whose code is 3. In this case, it's Code 3: 13, Form 144 \( \not \Rightarrow \) Form 206 whose summary information is:
    Hypothesis Statement
    Form 144 <p> Every set is almost well orderable. </p>

    Conclusion Statement
    Form 206 <p> The existence of a non-principal ultrafilter: There exists an infinite set \(X\) and a non-principal ultrafilter on \(X\). </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 1473, whose string of implications is:
    345 \(\Rightarrow\) 14 \(\Rightarrow\) 63 \(\Rightarrow\) 70 \(\Rightarrow\) 206

The conclusion Form 125 \( \not \Rightarrow \) Form 345 then follows.

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

Name Statement
\(\cal M15\) Feferman/Blass Model Blass constructs a model similar to Feferman's model, <a href="/models/Feferman-1">\(\cal M2\)</a>

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