Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
An ordinal analysis of admissible set theory using recursion on ordinal notations
 

Summary: An ordinal analysis of admissible set theory
using recursion on ordinal notations
Jeremy Avigad
May 23, 2001
Abstract
The notion of a function from N to N defined by recursion on ordinal
notations is fundamental in proof theory. Here this notion is generalized to
functions on the universe of sets, using notations for well-orderings longer
than the class of ordinals. The generalization is used to bound the rate
of growth of any function on the universe of sets that is 1-definable in
Kripke-Platek admissible set theory with an axiom of infinity. Formalizing
the argument provides an ordinal analysis.
1 Introduction
In informal proof-theoretic parlance, the definition of a set of objects is said to
be impredicative if it makes reference to a collection of sets that includes the
set being defined. A classic example arises if one takes the real numbers to be
lower Dedekind cuts of rationals, and then defines the least upper bound of a
bounded set of reals to be the intersection of all the upper bounds. A theory is
said to be (prima facie) impredicative if its intended interpretation depends on
such a definition.

  

Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University

 

Collections: Multidisciplinary Databases and Resources; Mathematics