Hypothesis: HR 141:
[14 P(\(n\))] with \(n = 2\): Let \(\{A(i): i\in I\}\) be a collection of sets such that \(\forall i\in I,\ |A(i)|\le 2\) and suppose \(R\) is a symmetric binary relation on \(\bigcup^{}_{i\in I} A(i)\) such that for all finite \(W\subseteq I\) there is an \(R\) consistent choice function for \(\{A(i): i \in W\}\). Then there is an \(R\) consistent choice function for \(\{A(i): i\in I\}\).
Conclusion: HR 110:
Every vector space over \(\Bbb Q\) has a basis.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N2^*(3)\) Howard's variation of \(\cal N2(3)\) | \(A=\bigcup B\), where\(B\) is a set of pairwise disjoint 3 element sets, \(T_i = \{a_i, b_i,c_i\}\) |
Code: 5
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