Vol. 83, No. 1, 1979

Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Chain conditions in free products of lattices with infinitary operations

George Grätzer, Andras Hajnal and David C. Kelly

Vol. 83 (1979), No. 1, 107–115
Abstract

There are many facts known about the size of subsets of certain kinds in free lattices and free products of lattices. Examples: every chain in a free lattice is at most countable; every “large” subset contains an independent set; if the free product of a set of lattices contains a “long” chain, so does the free product of a flnite subset of this set of lattices. Here we investigate these problems in the setting of a variety V of m-lattices, where m is an infinite regular cardinal. An m-lattice L is a lattice in which for any nonempty set S with |S| < m, the meet and join exist in L. We obtain generalizations of many finitary results to the m-complete case. Our basic set-theoretic tool is the Erdös-Rado theorem.

Mathematical Subject Classification 2000
Primary: 06B25
Milestones
Received: 21 March 1978
Revised: 29 December 1978
Published: 1 July 1979
Authors
George Grätzer
Andras Hajnal
David C. Kelly