Hypothesis: HR 14:
BPI: Every Boolean algebra has a prime ideal.
Conclusion: HR 17:
Ramsey's Theorem I: If \(A\) is an infinite set and the family of all 2 element subsets of \(A\) is partitioned into 2 sets \(X\) and \(Y\), then there is an infinite subset \(B\subseteq A\) such that all 2 element subsets of \(B\) belong to \(X\) or all 2 element subsets of \(B\) belong to \(Y\). (Also, see Form 325.), Jech [1973b], p 164 prob 11.20.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M1\) Cohen's original model | Add a denumerable number of generic reals (subsets of \(\omega\)), \(a_1\), \(a_2\), \(\cdots\), along with the set \(b\) containing them |
Code: 3
Comments: