Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 68, whose code is 4, is constructed around a proven non-implication as follows:

  • This non-implication was constructed without the use of this first code 2/1 implication.
  • A proven non-implication whose code is 3. In this case, it's Code 3: 1068, Form 163 \( \not \Rightarrow \) Form 146 whose summary information is:
    Hypothesis Statement
    Form 163 <p> Every non-well-orderable set has an infinite, Dedekind finite subset. </p>

    Conclusion Statement
    Form 146 <p> \(A(F,A1)\): For every \(T_2\) topological space \((X,T)\), if \(X\) is a continuous finite to one image of an A1 space then \((X,T)\) is  an A1 space. (\((X,T)\) is A1 means if \(U \subseteq  T\) covers \(X\) then \(\exists f : X\rightarrow U\) such that \((\forall x\in X) (x\in f(x)).)\) </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 4733, whose string of implications is:
    68 \(\Rightarrow\) 62 \(\Rightarrow\) 146

The conclusion Form 163 \( \not \Rightarrow \) Form 68 then follows.

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

Name Statement

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