2013/01/25 by Bowler, Nathan, Carmesin, Johannes
#03E60 #05B35 #05C63 #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1301.5980
Solving a problem of Diestel and Pott, we construct a large class of infinite matroids. These can be used to provide counterexamples against the natural extension of the Well-quasi-ordering-Conjecture to infinite matroids and to show that the class of planar infinite matroids does not have a universal matroid. The existence of these matroids has a connection to Set Theory in that it corresponds to the Determinacy of certain games. To show that our construction gives matroids, we introduce a new very simple axiomatization of the class of countable tame matroids.