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A cardinal pattern inspired by \(\text{AD}\). (English) Zbl 0857.03030
Let \(\Theta\) denote the least ordinal such that there is no function onto it which has the real line as domain. In a previous paper [“AD and patterns of singular cardinals below \(\Theta\)”, J. Symb. Logic 61, 225-235 (1996; Zbl 0855.03029)] the author gives a relative consistency result regarding the behaviour of the cofinality function below \(\Theta\); the consistency result is relative to the consistency of the Axiom of Determinacy. In particular, the author shows that modulo the consistency of the Axiom of Determinacy, a statement which implies that every uncountable regular cardinal number below \(\Theta\) is a (measurable – and thus) limit cardinal number is consistent.
In the present paper the author shows that if we assume a hypothesis stronger than the consistency of the Axiom of Determinacy but weaker than the existence of an almost huge cardinal number, then it is consistent that there is a proper class of regular cardinal numbers, and each regular cardinal number is a limit cardinal number.

MSC:
03E35 Consistency and independence results
03E55 Large cardinals
03E60 Determinacy principles
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