Form Classes

Statement:

Existence of a double uniformization: For all \(X\) and \(Y\), for all \(E\subseteq X\times Y\), if there is an infinite cardinal \(\kappa\) satisfying:

  1. \(\forall y_0\in Y\), \(|\{(x,y_0): x\in X\}\cap E| =\kappa\) and
  2. \(\forall x_0\in X\), \(|\{(x_0,y): y\in Y\}\cap E| = \kappa\),
then \(\exists U\subseteq E\) such that for all \((x,y)\in E, \exists !z\in X\) such that \((z,y)\in U\) and \(\exists !z\in Y\) such that \((x,z)\in U\). (\(U\) is called a double uniformization of \(E\).)

Howard_Rubin_Number: 184

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:
Kaniewski-Rogers-1980: Double uniformization

Book references

Note connections:

The following forms are listed as conclusions of this form class in rfb1: 93, 1,

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