Implications

• Implications Home
• Complete List
• Search

This non-implication, Form 133 \( \not \Rightarrow \) Form 292, 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: 355, Form 133 \( \not \Rightarrow \) Form 292 whose summary information is:
  

  Hypothesis	Statement
  Form 133	<p> Every set is either well orderable or has an infinite amorphous subset. </p>

  
  

  Conclusion	Statement
  Form 292	<p> \(MC(LO,\infty)\): For each linearly ordered family of non-empty sets \(X\), there is a function \(f\) such that for all \(x\in X\) \(f(x)\) is non-empty, finite subset of \(x\). </p>

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

The conclusion Form 133 \( \not \Rightarrow \) Form 292 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 \(A\)