Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 325, whose code is 4, 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 3. In this case, it's Code 3: 988, Form 163 \( \not \Rightarrow \) Form 124 whose summary information is:
    Hypothesis Statement
    Form 163 <p> Every non-well-orderable set has an infinite, Dedekind finite subset. </p>

    Conclusion Statement
    Form 124 <p> Every operator on a Hilbert space with an amorphous base is the direct sum of a finite matrix and  a  scalar operator.  (A set is <em>amorphous</em> if it is not the union of two disjoint infinite sets.) </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 1710, whose string of implications is:
    325 \(\Rightarrow\) 17 \(\Rightarrow\) 124

The conclusion Form 163 \( \not \Rightarrow \) Form 325 then follows.

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

Name Statement

Edit | Back