Implications

This non-implication, Form 416 \( \not \Rightarrow \) Form 79, 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: 9669, whose string of implications is:
    144 \(\Rightarrow\) 416
  • 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: 5885, whose string of implications is:
    79 \(\Rightarrow\) 70 \(\Rightarrow\) 206

The conclusion Form 416 \( \not \Rightarrow \) Form 79 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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