6 citations · 16 across the 9 of their papers we have counts for
9 papers
Asymptotic upper bounds on the shades of t-intersecting families
James Hirschorn
We examine the m-shades of t-intersecting families of k-subsets of [n], and conjecture on the optimal upper bound on their cardinalities. This conjecture extends Frankl's General C…
Nonhomogeneous analytic families of trees
James Hirschorn
We consider a dichotomy for analytic families of trees stating that either there is a colouring of the nodes for which all but finitely many levels of every tree are nonhomogeneous…
On the strength of Hausdorff's gap condition
James Hirschorn
Hausdorff's gap condition was satisfied by his original 1936 construction of an (omega-1,omega-1) gap in P(N)/Fin. We solve an open problem in determining whether Hausdorff's condi…
A strong antidiamond principle compatible with CH
James Hirschorn
A strong antidiamond principle (*c) is shown to be consistent with CH. This principle can be stated as a "P-ideal dichotomy": every P-ideal on omega-1 (i.e. an ideal that is sigma-…
Combinatorial and hybrid principles for sigma-directed families of countable sets modulo finite
James Hirschorn
We consider strong combinatorial principles for sigma-directed families of countable sets in the ordering by inclusion modulo finite, e.g. P-ideals of countable sets. We try for pr…
Partial order embeddings with convex range
James Hirschorn
A careful study is made of embeddings of posets which have a convex range. We observe that such embeddings share nice properties with the homomorphisms of more restrictive categori…