Ordinal Inequalities, Transfinite Induction, and Reverse Mathematics

Journal of Symbolic Logic 64 (2):769-774 (1999)
  Copy   BIBTEX

Abstract

If $\alpha$ and $\beta$ are ordinals, $\alpha \leq \beta$, and $\beta \nleq \alpha$, then $\alpha + 1 \leq \beta$. The first result of this paper shows that the restriction of this statement to countable well orderings is provably equivalent to ACA$_0$, a subsystem of second order arithmetic introduced by Friedman. The proof of the equivalence is reminiscent of Dekker's construction of a hypersimple set. An application of the theorem yields the equivalence of the set comprehension scheme ACA$_0$ and an arithmetical transfinite induction scheme.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,227

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Reverse Mathematics and Ordinal Multiplication.Jeffry L. Hirst - 1998 - Mathematical Logic Quarterly 44 (4):459-464.
Derived sequences and reverse mathematics.Jeffry L. Hirst - 1993 - Mathematical Logic Quarterly 39 (1):447-453.
Possible PCF algebras.Thomas Jech & Saharon Shelah - 1996 - Journal of Symbolic Logic 61 (1):313-317.
Consistency proof via pointwise induction.Toshiyasu Arai - 1998 - Archive for Mathematical Logic 37 (3):149-165.
Intuitionistically provable recursive well-orderings.Harvey M. Friedman & Andre Scedrov - 1986 - Annals of Pure and Applied Logic 30 (2):165-171.
Variation on a theme of Schutte.D. Probst & G. Jager - 2004 - Mathematical Logic Quarterly 50 (3):258.

Analytics

Added to PP
2017-02-21

Downloads
2 (#1,807,551)

6 months
1 (#1,477,342)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references