Implications

We have the following indirect implication of form equivalence classes:

274 \(\Rightarrow\) 274
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
274 \(\Rightarrow\) 274

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
274:

There is a cardinal number \(x\) and an \(n\in\omega\) such that \(\neg(x\) adj\(^n\, x^2)\). (The expression ``\(x\) adj\(^n\, ya\)" means there are cardinals \(z_0,\ldots, z_n\) such that \(z_0 = x\) and \(z_n = y\) and for all \(i,\ 0\le i < n,\ z_i< z_{i+1}\) and if  \(z_i < z\le z_{i+1}\), then \(z = z_{i+1}.)\) (Compare with [0 A]).

274:

There is a cardinal number \(x\) and an \(n\in\omega\) such that \(\neg(x\) adj\(^n\, x^2)\). (The expression ``\(x\) adj\(^n\, ya\)" means there are cardinals \(z_0,\ldots, z_n\) such that \(z_0 = x\) and \(z_n = y\) and for all \(i,\ 0\le i < n,\ z_i< z_{i+1}\) and if  \(z_i < z\le z_{i+1}\), then \(z = z_{i+1}.)\) (Compare with [0 A]).

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