Conservativity of an ultrafilter of IP sets over \a0
Conservativity of an ultrafilter of IP sets over \a0
An IP set is a set of natural numbers containing all finite sums of an infinite sequence of natural numbers. Let be an ultrafilter on , and let denote the corresponding subsystem of second-order arithmetic. IP-ultrafilter conservativity conjecture. The theory
is a conservative extension of . This asks whether the existence of an ultrafilter all of whose members are IP sets adds no first-order consequences to ; the source presents the claim in the context of the difficulty of separating Hindman's-type principles from , and gives no resolution.
Sources & referencesView supporting material
Primary source
Henry Towsner, “Ultrafilters in Reverse Mathematics”, arXiv:1109.3902 (2011).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.