Implications

This non-implication, Form 283 \( \not \Rightarrow \) Form 407, 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: 2077, whose string of implications is:
    49 \(\Rightarrow\) 30 \(\Rightarrow\) 62 \(\Rightarrow\) 283
  • A proven non-implication whose code is 5. In this case, it's Code 3: 118, Form 49 \( \not \Rightarrow \) Form 14 whose summary information is:
    Hypothesis Statement
    Form 49 <p> <strong>Order Extension Principle:</strong> Every partial ordering can be extended to a linear ordering.  <a href="/articles/Tarski-1924">Tarski [1924]</a>, p 78. </p>

    Conclusion Statement
    Form 14 <p> <strong>BPI:</strong> Every Boolean algebra has a prime ideal. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 9601, whose string of implications is:
    407 \(\Rightarrow\) 14

The conclusion Form 283 \( \not \Rightarrow \) Form 407 then follows.

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

Name Statement
\(\cal N52\) Felgner/Truss Model Let \((\cal B,\prec)\) be a countableuniversal homogeneous linearly ordered Boolean algebra, (i.e., \(<\) is alinear ordering extending the Boolean partial ordering on \(B\))

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