Minimal Antichains in Well-founded Quasi-orders with an Application to Tournaments

Authors: Cherlin G.L.1; Latka B.J.2

Source: Journal of Combinatorial Theory, Series B, Volume 80, Number 2, November 2000 , pp. 258-276(19)

Publisher: Academic Press

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content

Abstract:

We investigate the minimal antichains (in what is essentially Nash-Williams' sense) in a well-founded quasi-order. We prove the following finiteness theorem: If Q is a well-founded quasi-order and k a fixed natural number, then there is a finite set Lambdak of minimal antichains of Q with the property that for any ideal I of Q obtained by excluding at most k elements of Q, I is well-quasi-ordered if and only if its intersection with each antichain in Lambdak is finite. When applied in a suitably sharpened form to an algorithmic problem arising in model theory, this yields a strengthening of the main result of [18]. Copyright 2000 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, Hill Center, Rutgers University, Piscataway, New Jersey, 08855 2: Department of Mathematics, Lafayette College, Easton, Pennsylvania, 18042

The full text electronic article is available for purchase. You will be able to download the full text electronic article after payment.

$54.13 plus tax      Refund Policy

 

OR

Back to top

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content
Share this item with others: These icons link to social bookmarking sites where readers can share and discover new web pages.
Page Help Click here for Page Help
Shopping cart
Tools
Sign in






Need to register?
Sign up here
Text size: A | A | A | A