6 citations · 16 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
Random gaps
James Hirschorn
It is proved that there exists an (omega-1,omega-1) Souslin gap in the Boolean algebra (L(nu)/Fin,subseteq^*_ae) for every nonseparable measure nu. Thus a Souslin, also known as de…
Some partition properties for measurable colourings of omega-one^2
James Hirschorn
We construct a measure on omega-one^2 over the ground model in the forcing extension of a measure algebra, and investigate when measure theoretic properties of some measurable colo…