Axiom Of Choice

Cohen \(\cal M16(n)\): Monro's Model I | Historical notes

Description: Monro has constructed an \(\omega\)-sequence of models of \(ZF\) such that,

(*) For each ordinal \(\alpha\), \(\cal P^n(\alpha)\) is the same in the \(n\)th model and the \(n+1\)st model.

(\(\cal P^0(\alpha)=\alpha,\) and \(\cal P^{n+1}(\alpha)=\cal P(\cal P^n(\alpha))\).) He starts with a countable transitive model \(\cal M\models ZF + V = L\)

Parameter(s): This model depends on the following parameter(s): \(n\), \(n\): non-negative integer

All Forms Known to be True in \(\cal M16(n)\):
0,

All Forms Known to be False in \(\cal M16(n)\):
430-p, 427, 391, 335-n, 334, 333, 292, 264, 239, 218, 202, 164, 149, 147, 133, 114, 112, 109, 95-F, 91, 90, 89, 81-n, 67, 66, 28-p, 15, 1,

A minimial list of forms whose truth in this model imply all others that are true in this model: 0

Falses that are implied by others list: 15-81-91

References for models trues falses list: ReferencesMonro [1972], \cite{1973b}, Note 18.

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