Playing with admissibility spectra
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Jensen showed that any countable sequenceA ofA-admissibles is the initial part of the admissibility spectrum of a realR. His construction generalizes straightforwardly to Σ n -admissibles. This adaptation makes admissibles not inA R-inadmissible. We strengthen Jensen’s theorem by requiring that Σ n (A)-admissibles not inA be Σ m (R)-admissible or Σ m (R)-non-projectible, form <n.
KeywordsExtension Property Closure Property Countable Sequence Large Cardinal Skolem Function
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