Recursively mahlo ordinals and inductive definitions

Wayne Richter

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


This chapter discusses the recursively Mahlo ordinals and inductive definitions. A characterization of the first recursively Mahlo ordinal and the first recursively hyper-Mahlo ordinalis provided. The large countable ordinals are obtained as the closure ordinals of inductive definitions. Inductive definitions play a central role in hierarchy theory. A classic example is the theory of recursive ordinals. The usual systems of notations for the recursive ordinals are inductively defined by very simple (arithmetic) operations. A version of the Candy theorem on the existence of selection operators is the basic tool. A typical system is defined by an inductive definition consisting of several cases, depending on whether the ordinal reached at a given stage was zero, a successor, notationally singular, and notationally regular.

Original languageEnglish (US)
Pages (from-to)273-288
Number of pages16
JournalStudies in Logic and the Foundations of Mathematics
Issue numberC
StatePublished - Jan 1 1971

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