Inductive Definitions and Reflecting Properties of Admissible Ordinals

Wayne Richter, Peter Aczel

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

This chapter focuses on how to formulate constructive analogues for large regular ordinals and how to obtain notation systems for them using non-monotone inductive definitions. The chapter presents results locating the ordinals of inductive definitions in relation to the ordinals of certain wellorderings. Alternative characterizations of some of the reflecting properties of admissible ordinals are presented. The chapter presents a comparative analysis of reflecting properties of admissible ordinals with the reflecting properties for the indescribable cardinals, and investigate their relative magnitudes. The chapter examines the first order inductive definitions. The notion of a closed class of operators is formulated. The construction of the notation systems and the associated coding lemma are the key to getting lower bounds for the ordinals of inductive definitions. The coding lemma is proved in the chapter.

Original languageEnglish (US)
Pages (from-to)301-381
Number of pages81
JournalStudies in Logic and the Foundations of Mathematics
Volume79
Issue numberC
DOIs
StatePublished - Jan 1 1974

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