Skip header navigation

University of Stirling

×

Book Chapter

Structures, homomorphisms, and the needs of model theory

Citation
Milne P (2015) Structures, homomorphisms, and the needs of model theory. In: Arazim P & Dancak M (eds.) Logica Yearbook 2014. The Logica Yearbook. London: College Publications, pp. 215-231. http://logika.flu.cas.cz/en/logica-yearbook/logica-yearbook

Abstract
When we look closely at textbooks on model theory, we find that there are three different accounts of what a model or structure is. One of these is highly language dependent, so that the same structure cannot be the interpretation of two different languages or signatures. The other two definitions do not fall foul of that dependence but all textbooks tie the notion of homomorphism so closely to language (signature) that only structures interpreting the same language (signature) are isomorphic. Although this follows the practice in universal algebra, it is highly unnatural. The aim here is to present a notion of homomorphism better consonant with intuition and with what the less cautious authors of textbooks say when they speak informally.

Keywords
Model theory; structures; homomorphisms

StatusPublished
Author(s)Milne, Peter
Title of seriesThe Logica Yearbook
Publication date31/12/2015
URLhttp://hdl.handle.net/1893/21978
PublisherCollege Publications
Publisher URLhttp://logika.flu.cas.cz/en/logica-yearbook/logica-yearbook
Place of publicationLondon
ISBN978-1-84890-177-3
Scroll back to the top