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This non-implication, Form 233 \( \not \Rightarrow \) Form 64, 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: 554, Form 233 \( \not \Rightarrow \) Form 64 whose summary information is:
  

  Hypothesis	Statement
  Form 233	<p> <strong>Artin-Schreier theorem:</strong> If a field has an algebraic closure it is unique up to isomorphism. </p>

  
  

  Conclusion	Statement
  Form 64	<p> \(E(I,Ia)\) There are no amorphous sets. (Equivalently, every infinite set is the union of two disjoint infinite sets.) </p>

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

The conclusion Form 233 \( \not \Rightarrow \) Form 64 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 \(A\)