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This non-implication, Form 132 \( \not \Rightarrow \) Form 278, 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: 9938, whose string of implications is: 380 \(\Rightarrow\) 132
• A proven non-implication whose code is 5. In this case, it's Code 3: 745, Form 380 \( \not \Rightarrow \) Form 278 whose summary information is:
  

  Hypothesis	Statement
  Form 380	<p> \(PC(\infty,WO,\infty)\):  For every infinite family of non-empty well orderable sets, there is an infinite subfamily \(Y\) of \(X\) which has a choice function. </p>

  
  

  Conclusion	Statement
  Form 278	<p> In an integral domain \(R\), if every ideal is finitely generated then \(R\) has a maximal proper ideal. <a href="/notes/note-45">note 45</a> E. </p>

  
  
• This non-implication was constructed without the use of this last code 2/1 implication

The conclusion Form 132 \( \not \Rightarrow \) Form 278 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 \(A\)