Statement:
Let \(\Omega\) be the set of all (undirected) infinite cycles of reals (Graphs whose vertices are real numbers, connected, no loops and each vertex adjacent to exactly two others). Then there is a function \(f\) on \(\Omega \) such that for all \(s\in\Omega\), \(f(s)\) is a direction along \(s\).
Howard_Rubin_Number: 140
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Truss-1984: Cancellation laws for surjective cardinals
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 140 A | (Form 137 with \(k = 2\)): If \(f\) is a 1-1 map from \(2\times X\) into \(2\times Y\) then there are partitions \(X = X_0 \cup X_1\) and \(Y = Y_0 \cup Y_1\) of \(X\) and \(Y\) such that \(f\) maps \((\{0\}\times X_0)\cup (\{1\}\times X_1)\) onto \((\{0\}\times Y_0)\cup (\{1\}\times Y_1)\). |
Truss [1984]
|