Implications

This non-implication, Form 211 \( \not \Rightarrow \) Form 233, whose code is 6, is constructed around a proven non-implication as follows:
Note: This non-implication is actually a code 4, as this non-implication satisfies the transferability criterion. Click Transfer details for all the details)

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 6183, whose string of implications is:
    91 \(\Rightarrow\) 79 \(\Rightarrow\) 203 \(\Rightarrow\) 211
  • A proven non-implication whose code is 5. In this case, it's Code 3: 223, Form 91 \( \not \Rightarrow \) Form 241 whose summary information is:
    Hypothesis Statement
    Form 91 <p> \(PW\):  The power set of a well ordered set can be well ordered. </p>

    Conclusion Statement
    Form 241 <p> Every algebraic closure of \(\Bbb Q\) has a real closed subfield. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 7879, whose string of implications is:
    233 \(\Rightarrow\) 242 \(\Rightarrow\) 241

The conclusion Form 211 \( \not \Rightarrow \) Form 233 then follows.

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

Name Statement
\(\cal N31\) L&auml;uchli's Model IV The set \(A\) is denumerable

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