Implications

This non-implication, Form 249 \( \not \Rightarrow \) Form 421, 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: 1175, whose string of implications is:
    32 \(\Rightarrow\) 10 \(\Rightarrow\) 249
  • A proven non-implication whose code is 3. In this case, it's Code 3: 846, Form 32 \( \not \Rightarrow \) Form 338 whose summary information is:
    Hypothesis Statement
    Form 32 <p> \(C(\aleph_0,\le\aleph_0)\): Every denumerable set of non-empty countable sets  has a choice function. </p>

    Conclusion Statement
    Form 338 <p> \(UT(\aleph_0,\aleph_0,WO)\): The union of a denumerable number of denumerable sets is well orderable. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 9989, whose string of implications is:
    421 \(\Rightarrow\) 338

The conclusion Form 249 \( \not \Rightarrow \) Form 421 then follows.

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

Name Statement

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