Form Classes

Form equivalence class Howard-Rubin Number: 86-alpha

Statement:

If \((P,\le)\) is a tree of height \(\lambda\le \aleph_\alpha\) which has fewer than \(\lambda\) branches of height \(<\lambda\) then one of the following holds for the upside down tree \((P,\ge)\):

  1. There is a cardinal \(\mu< \lambda\) such that \((P,\ge)\) does not contain a strong antichain of cardinality \(\mu\).
  2. \((P,\ge)\) contains a strong antichain of cardinality \(\lambda\).
  3. \((P,\ge)\) contains a chain of cardinality \(\lambda\).

Howard-Rubin number: 86A-alpha

Citations (articles): Shannon [1992] A note on some weak forms of the axiom of choice

Connections (notes): Note [119] Definitions from Shannon [1992] for form [86 A(\(\alpha\))]

References (books):

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