Form Classes

Statement:

There are no \(\aleph_{\alpha}\) minimal  sets.  That is, there are no sets \(X\) such that

  1. \(|X|\) is incomparable with \(\aleph_{\alpha}\)
  2. \(\aleph_{\beta}<|X|\) for every \(\beta < \alpha \) and
  3. \(\forall Y\subseteq X, |Y|<\aleph_{\alpha}\) or \(|X-Y| <\aleph_{\alpha}\).

Howard_Rubin_Number: 183-alpha

Parameter(s): This form depends on the following parameter(s): \(\beta\), \(\beta\): ordinal number

This form's transferability is: Unknown

This form's negation transferability is: Negation Transferable

Article Citations:
Hickman-1980b: \(\Lambda\) - minimal lattices

Book references

Note connections:
Note 56 Hickman [1980b] generalizes the notion of amorphous.

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

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