Implications

This non-implication, Form 313 \( \not \Rightarrow \) Form 189, 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: 9696, whose string of implications is:
    91 \(\Rightarrow\) 313
  • A proven non-implication whose code is 5. In this case, it's Code 3: 213, Form 91 \( \not \Rightarrow \) Form 190 whose summary information is:
    Hypothesis Statement
    Form 91 <p> \(PW\):  The power set of a well ordered set can be well ordered. </p>

    Conclusion Statement
    Form 190 <p> There is a non-trivial injective Abelian group. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 9616, whose string of implications is:
    189 \(\Rightarrow\) 190

The conclusion Form 313 \( \not \Rightarrow \) Form 189 then follows.

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

Name Statement
\(\cal N28\) Blass' Permutation Model The set \(A=\{a^i_{\xi}: i\in \Bbb Z, \xi\in\aleph_1\}\)

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