Form Classes

Statement:

There is a partition of the real line into \(\aleph_1\) Borel sets \(\{B_\alpha: \alpha<\aleph_1\}\) such that for some \(\beta <\aleph_1\), \(\forall\alpha <\aleph_1\), \(B_{\alpha}\in G_{\beta}\). (\(G_\beta\) for \(\beta < \aleph_1\) is defined by induction, \(G_0=\{A: A\) is an open subset of \({\Bbb R}\}\) and for \(\beta > 0\),

  • \(G_\beta =\left\{\bigcup^\infty_{i=0}A_{i}: (\forall i\in\omega) (\exists\xi <\beta)(A_i\in G_\xi)\,\right\}\) if \(\beta\) is even and
  • \(G_\beta = \left\{\bigcap^\infty_{i=0}A_{i}: (\forall i\in\omega) (\exists \xi < \beta)(A_{i}\in G_\xi)\,\right\}\) if \(\beta\) is odd.)

Howard_Rubin_Number: 224

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:
Stern-1979: Suites transfinies d'ensemble boreliens

Book references

Note connections:

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

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