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A direct proof of the five element basis theorem
Aronszajn trees Countryman type forcing axioms
2011/1/17
We present a direct proof of the consistency of the existence of a five element basis for the uncountable linear orders. Our argument is based on the approach of [9] and simplifies the original proof ...
Sparse paving matroids, basis-exchange properties, and cyclic flats
Sparse paving matroids basis-exchange properties cyclic flats
2010/11/9
We provide evidence for five long-standing, basis-exchange conjectures for matroids by proving them for the enormous class of sparse paving matroids. We also explore the role that these matroids may p...