Yes, the "missing axiom" of matroid theory is lost forever
Combinatorics
2017-03-03 v3
Abstract
We prove there is no sentence in the monadic second-order language MS0 that characterises when a matroid is representable over at least one field, and no sentence that characterises when a matroid is K-representable, for any infinite field K. By way of contrast, because Rota's Conjecture is true, there is a sentence that characterises F-representable matroids, for any finite field F.
Cite
@article{arxiv.1412.8399,
title = {Yes, the "missing axiom" of matroid theory is lost forever},
author = {Dillon Mayhew and Mike Newman and Geoff Whittle},
journal= {arXiv preprint arXiv:1412.8399},
year = {2017}
}
Comments
26 pages, 3 figures, this version features revisions of two proofs