2014/12/29 by Mayhew, Dillon, Newman, Mike, Whittle, Geoff · 1 citation
#05B35 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1412.8399
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.