TY - JOUR

T1 - Recursively mahlo ordinals and inductive definitions

AU - Richter, Wayne

PY - 1971/1/1

Y1 - 1971/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79959420994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959420994&partnerID=8YFLogxK

U2 - 10.1016/S0049-237X(08)71233-3

DO - 10.1016/S0049-237X(08)71233-3

M3 - Article

AN - SCOPUS:79959420994

VL - 61

SP - 273

EP - 288

JO - Studies in Logic and the Foundations of Mathematics

JF - Studies in Logic and the Foundations of Mathematics

SN - 0049-237X

IS - C

ER -