Implications

This non-implication, Form 130 \( \not \Rightarrow \) Form 10, 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: 9692, whose string of implications is:
    91 \(\Rightarrow\) 130
  • 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: 10244, whose string of implications is:
    10 \(\Rightarrow\) 249

The conclusion Form 130 \( \not \Rightarrow \) Form 10 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

Edit | Back