Title

Obstacles to Duality between Classes of Relational Structures

Document Type

Article

Language

eng

Format of Original

5 p.

Publication Date

12-1983

Publisher

Springer

Source Publication

Algebra Universalis

Source ISSN

0002-5240

Original Item ID

doi: 10.1007/BF01194516

Abstract

We prove an algebraic result concerning inverse limits of copowers in anS-class of relational structures of the same (finitary or infinitary) type. Among several applications to the nonexistence of category dualities is the following Theorem: If there exist arbitrarily large measurable cardinals then any classK of relational structures containing a nontrivial objectA and all of its cartesian powers via nonempty index sets will fail to be dual to anyS-class. (No large cardinal assumption is necessary if either there is a finite suchA or ifK consists only of finitary relational structures and contains the elementary class generated byA and its cartesian powers).

Comments

Algebra Universalis, Vol. 17, No. 1 (December 1983): 87-91. DOI.