Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 270, 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: 4742, whose string of implications is:
    270 \(\Rightarrow\) 62 \(\Rightarrow\) 146

The conclusion Form 163 \( \not \Rightarrow \) Form 270 then follows.

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

Name Statement

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