Combinatorics with definable sets: Euler characteristics and grothendieck rings

Bulletin of Symbolic Logic 6 (3):311-330 (2000)
We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex numbers contains as a subring the ring of integer polynomials in continuum many variables. We prove the existence of a universal strong Euler characteristic on a structure. We investigate the dependence of the Grothendieck ring on the theory of the structure and give a few counter-examples. Finally, we relate some open problems and independence results in bounded arithmetic to properties of particular Grothendieck rings.
Keywords First Order Structure   Euler Characteristic   Grothendieck Ring
Categories (categorize this paper)
DOI 10.2307/421058
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 15,865
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Roman Wencel (2008). Weakly o-Minimal Nonvaluational Structures. Annals of Pure and Applied Logic 154 (3):139-162.
Amit Kuber (2015). Grothendieck Rings of Theories of Modules. Annals of Pure and Applied Logic 166 (3):369-407.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

9 ( #245,889 of 1,725,153 )

Recent downloads (6 months)

2 ( #268,621 of 1,725,153 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.