Implications

This non-implication, Form 415 \( \not \Rightarrow \) Form 335-n, 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: 9668, whose string of implications is:
    144 \(\Rightarrow\) 415
  • A proven non-implication whose code is 5. In this case, it's Code 3: 412, Form 144 \( \not \Rightarrow \) Form 294 whose summary information is:
    Hypothesis Statement
    Form 144 <p> Every set is almost well orderable. </p>

    Conclusion Statement
    Form 294 <p> Every linearly ordered \(W\)-set is well orderable. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 9198, whose string of implications is:
    335-n \(\Rightarrow\) 333 \(\Rightarrow\) 67 \(\Rightarrow\) 89 \(\Rightarrow\) 90 \(\Rightarrow\) 51 \(\Rightarrow\) 294

The conclusion Form 415 \( \not \Rightarrow \) Form 335-n then follows.

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

Name Statement
\(\cal N41\) Another variation of \(\cal N3\) \(A=\bigcup\{B_n; n\in\omega\}\)is a disjoint union, where each \(B_n\) is denumerable and ordered like therationals by \(\le_n\)

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