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This non-implication, Form 380 \( \not \Rightarrow \) Form 69, whose code is 6, 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 5. In this case, it's Code 3: 740, Form 380 \( \not \Rightarrow \) Form 69 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 69	<p> Every field has an algebraic closure.  <a href="/books/8">Jech [1973b]</a>, p 13. <p>

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

The conclusion Form 380 \( \not \Rightarrow \) Form 69 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 \(A\)