The metamathematics of scattered linear orderings

Archive for Mathematical Logic 29 (1):9-20 (1989)
  Copy   BIBTEX


Pursuing the proof-theoretic program of Friedman and Simpson, we begin the study of the metamathematics of countable linear orderings by proving two main results. Over the weak base system consisting of arithmetic comprehension, II 1 1 -CA0 is equivalent to Hausdorff's theorem concerning the canonical decomposition of countable linear orderings into a sum over a dense or singleton set of scattered linear orderings. Over the same base system, ATR0 is equivalent to a version of the Continuum Hypothesis for linear orderings, which states that every countable linear ordering either has countably many or continuum many Dedekind cuts



    Upload a copy of this work     Papers currently archived: 74,466

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A Coding of the Countable Linear Orderings.Patrick Dehornoy - 1990 - Studia Logica 49 (4):585 - 590.
A Recursion Principle for Linear Orderings.Juha Oikkonen - 1992 - Journal of Symbolic Logic 57 (1):82-96.
Countably Categorical Coloured Linear Orders.Feresiano Mwesigye & John K. Truss - 2010 - Mathematical Logic Quarterly 56 (2):159-163.
Up to Equimorphism, Hyperarithmetic Is Recursive.Antonio Montalbán - 2005 - Journal of Symbolic Logic 70 (2):360 - 378.
On the Equimorphism Types of Linear Orderings.Antonio Montalbán - 2007 - Bulletin of Symbolic Logic 13 (1):71-99.
A Construction for Recursive Linear Orderings.C. J. Ash - 1991 - Journal of Symbolic Logic 56 (2):673-683.
Necessary Use of [Image] Induction in a Reversal.Itay Neeman - 2011 - Journal of Symbolic Logic 76 (2):561 - 574.
Cognitive Processing of Linear Orderings.Karl W. Scholz & George R. Potts - 1974 - Journal of Experimental Psychology 102 (2):323.


Added to PP

13 (#760,222)

6 months
1 (#417,143)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Up to Equimorphism, Hyperarithmetic Is Recursive.Antonio Montalbán - 2005 - Journal of Symbolic Logic 70 (2):360 - 378.
Reverse Mathematics and Initial Intervals.Emanuele Frittaion & Alberto Marcone - 2014 - Annals of Pure and Applied Logic 165 (3):858-879.
Borel Quasi-Orderings in Subsystems of Second-Order Arithmetic.Alberto Marcone - 1991 - Annals of Pure and Applied Logic 54 (3):265-291.

Add more citations

References found in this work

No references found.

Add more references