Hypothesis: HR 14:
BPI: Every Boolean algebra has a prime ideal.
Conclusion: HR 155: \(LC\): There are no non-trivial Läuchli continua. (A Läuchli continuum is a strongly connected continuum. Continuum \(\equiv\) compact, connected, Hausdorff space; and strongly connected \(\equiv\) every continuous real valued function is constant.)
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N3\) Mostowski's Linearly Ordered Model | \(A\) is countably infinite;\(\precsim\) is a dense linear ordering on \(A\) without first or lastelements (\((A,\precsim) \cong (\Bbb Q,\le)\)); \(\cal G\) is the group of allorder automorphisms on \((A,\precsim)\); and \(S\) is the set of all finitesubsets of \(A\) |
Code: 3
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