Implications

This non-implication, Form 139 \( \not \Rightarrow \) Form 57, 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: 6836, whose string of implications is:
    147 \(\Rightarrow\) 91 \(\Rightarrow\) 79 \(\Rightarrow\) 139
  • A proven non-implication whose code is 5. In this case, it's Code 3: 417, Form 147 \( \not \Rightarrow \) Form 64 whose summary information is:
    Hypothesis Statement
    Form 147 <p> \(A(D2)\):  Every \(T_2\) topological space \((X,T)\) can be covered by a well ordered family of discrete sets. </p>

    Conclusion Statement
    Form 64 <p> \(E(I,Ia)\) There are no amorphous sets. (Equivalently, every infinite set is the union of two disjoint infinite sets.) </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 9885, whose string of implications is:
    57 \(\Rightarrow\) 64

The conclusion Form 139 \( \not \Rightarrow \) Form 57 then follows.

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

Name Statement
\(\cal N1\) The Basic Fraenkel Model The set of atoms, \(A\) is denumerable; \(\cal G\) is the group of all permutations on \(A\); and \(S\) isthe set of all finite subsets of \(A\)

Edit | Back