A logical approach to abstract algebra

Authors:
Thierry Coquand;Henri Lombardi
Affiliations:
Computer Science and Engineering, Chalmers University of Technology and Göteborg University, 412 96 Göteborg, Sweden Email: coquand@cs.chalmers.se;Computer Science and Engineering, Chalmers University of Technology and Göteborg University, 412 96 Göteborg, Sweden Email: coquand@cs.chalmers.se
Venue:
Mathematical Structures in Computer Science
Year:
2006

Citing 0
Cited 4

A Mechanized Proof of the Basic Perturbation Lemma

Journal of Automated Reasoning
Spectral schemes as ringed lattices

Annals of Mathematics and Artificial Intelligence
Noetherian orders

Mathematical Structures in Computer Science
Induction in Algebra: A First Case Study

LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Recent work in constructive mathematics shows that Hilbert's program works for a large part of abstract algebra. Using in an essential way the ideas contained in the classical arguments, we can transform most of the highly abstract proofs of ‘concrete’ statements into elementary proofs. Surprisingly, the arguments we produce are not only elementary but also mathematically clearer, and not necessarily longer. We present an example where the simplification was significant enough to suggest an improved version of a classical theorem. For this we use a general method to transform some logically complex first-order formulae into a geometrical form, which may be interesting in itself.