The order types of termination orderings on monadic terms, strings and multisets

Journal of Symbolic Logic 62 (2):624-635 (1997)

We consider total well-founded orderings on monadic terms satisfying the replacement and full invariance properties. We show that any such ordering on monadic terms in one variable and two unary function symbols must have order type ω, ω 2 or ω ω . We show that a familiar construction gives rise to continuum many such orderings of order type ω. We construct a new family of such orderings of order type ω 2 , and show that there are continuum many of these. We show that there are only four such orderings of order type ω ω , the two familiar recursive path orderings and two closely related orderings. We consider also total well-founded orderings on N n which are preserved under vector addition. We show that any such ordering must have order type ω k for some 1 ≤ k ≤ n. We show that if $k there are continuum many such orderings, and if k = n there are only n!, the n! lexicographic orderings
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275551
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 47,330
Through your library

References found in this work BETA

Introduction to the Foundations of Mathematics.Ernest Nagel - 1953 - Journal of Philosophy 50 (19):591-593.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

A Unification Algorithm for Second-Order Monadic Terms.William M. Farmer - 1988 - Annals of Pure and Applied Logic 39 (2):131-174.
Belief Revision and Verisimilitude.Mark Ryan & Pierre-Yves Schobbens - 1995 - Notre Dame Journal of Formal Logic 36 (1):15-29.
Order-Isomorphic Η 1 -Orderings in Cohen Extensions.Bob A. Dumas - 2009 - Annals of Pure and Applied Logic 158 (1-2):1-22.
Strong Termination for the Epsilon Substitution Method.Grigori Mints - 1996 - Journal of Symbolic Logic 61 (4):1193-1205.
Dialect Variants and Linguistic Deviance.Ronald R. Butters - 1971 - Foundations of Language 7 (2):239-254.
Involutions Defined by Monadic Terms.Renato A. Lewin - 1988 - Studia Logica 47 (4):387 - 389.
Value Relations Revisited.Wlodek Rabinowicz - 2012 - Economics and Philosophy 28 (2):133-164.


Added to PP index

Total views
14 ( #628,557 of 2,291,031 )

Recent downloads (6 months)
1 ( #833,703 of 2,291,031 )

How can I increase my downloads?


My notes

Sign in to use this feature