Implications

This non-implication, Form 364 \( \not \Rightarrow \) Form 132, 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: 6902, whose string of implications is:
    91 \(\Rightarrow\) 363 \(\Rightarrow\) 364
  • A proven non-implication whose code is 5. In this case, it's Code 3: 226, Form 91 \( \not \Rightarrow \) Form 249 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 249 <p> If \(T\) is an infinite tree in which every element has exactly 2 immediate successors then \(T\) has an infinite branch. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 1128, whose string of implications is:
    132 \(\Rightarrow\) 10 \(\Rightarrow\) 249

The conclusion Form 364 \( \not \Rightarrow \) Form 132 then follows.

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

Name Statement
\(\cal N35\) Truss' Model IV The set of atoms, \(A\), is denumerable andeach element of \(A\) is associated with a finite sequence of zeros andones

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