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This non-implication, Form 374-n \( \not \Rightarrow \) Form 422-n, whose code is 4, is constructed around a proven non-implication as follows:

• An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 3985, whose string of implications is: 47-n \(\Rightarrow\) 423 \(\Rightarrow\) 374-n
• A proven non-implication whose code is 3. In this case, it's Code 3: 283, Form 47-n \( \not \Rightarrow \) Form 422-n whose summary information is:
  

  Hypothesis	Statement
  Form 47-n	<p> If \(n\in\omega-\{0,1\}\), \(C(WO,n)\): Every well ordered collection of \(n\)-element sets has a choice function. </p>

  
  

  Conclusion	Statement
  Form 422-n	<p> \(UT(WO,n,WO)\), \(n\in \omega-\{0,1\}\): The union of a well ordered set of \(n\) element sets can be well ordered. </p>

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

The conclusion Form 374-n \( \not \Rightarrow \) Form 422-n then follows.

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

Name	Statement
\(\cal N22(p)\) Makowski/Wi\'sniewski/Mostowski Model	(Where \(p\) is aprime) Let \(A=\bigcup\{A_i: i\in\omega\}\) where The \(A_i\)'s are pairwisedisjoint and each has cardinality \(p\)