Implications

This non-implication, Form 0 \( \not \Rightarrow \) Form 278, 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: 105, Form 0 \( \not \Rightarrow \) Form 244 whose summary information is:
    Hypothesis Statement
    Form 0  \(0 = 0\).

    Conclusion Statement
    Form 244 <p> Every principal ideal domain has a maximal ideal. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 10232, whose string of implications is:
    278 \(\Rightarrow\) 244

The conclusion Form 0 \( \not \Rightarrow \) Form 278 then follows.

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

Name Statement
\(\cal N31\) L&auml;uchli's Model IV The set \(A\) is denumerable

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