Implications

This non-implication, Form 0 \( \not \Rightarrow \) 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: 176, Form 0 \( \not \Rightarrow \) Form 210 whose summary information is:
    Hypothesis Statement
    Form 0  \(0 = 0\).

    Conclusion Statement
    Form 210 <p> The commutator subgroup of a free group is free. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 10220, whose string of implications is:
    68 \(\Rightarrow\) 210

The conclusion Form 0 \( \not \Rightarrow \) Form 68 then follows.

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

Name Statement
\(\cal N30\) L&auml;uchli's Model III The set \(A\) is denumerable; \(\cal G\) isthe group generated by the set of transpositions on \(A\); and \(S\) is theset of all finite subsets of \(A\)

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