Implications

This non-implication, Form 10 \( \not \Rightarrow \) Form 133, 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: 10083, whose string of implications is:
    32 \(\Rightarrow\) 10
  • 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: 7594, whose string of implications is:
    133 \(\Rightarrow\) 231 \(\Rightarrow\) 338

The conclusion Form 10 \( \not \Rightarrow \) Form 133 then follows.

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

Name Statement

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