BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Heidi Benham (University of Connecticut) DTSTART:20250424T180000Z DTEND:20250424T190000Z DTSTAMP:20260423T035932Z UID:OLS/177 DESCRIPTION:Title: Pr oblem Reducibility of Weakened Ginsburg—Sands Theorem\nby Heidi Benh am (University of Connecticut) as part of Online logic seminar\n\n\nAbstra ct\nA recent paper by Benham\, DeLapo\, Dzhafarov\, Solomon\, and Villano entitled “Ginsburg—Sands theorem and computability theory” analyzes computability theoretical and reverse mathematical strength of a topologic al theorem by Ginsburg and Sands\, along with several weakened versions. T he original theorem states that every infinite topological space has an in finite subspace homeomorphic to one of the following on the natural number s: indiscrete\, initial segment\, final segment\, discrete\, or cofinite. In this original paper\, it is claimed that the theorem is a consequence o f Ramsey’s Theorem\, and though it has been shown by Benham\, DeLapo\, D zhafarov\, Solomon\, and Villano that the full theorem is equivalent over RCA_0 to ACA_0\, there is a weakened version that is equivalent over RCA_0 to CAC (Chain-antichain Principle)\, a consequence of Ramsey’s Theorem. One interesting feature of the proof of this equivalence is that\, not on ly an application CAC\, but also an application of ADS (Ascending/descendi ng Sequence Principle)\, which is a consequence of CAC\, is used. This ins pires the question of whether this weakened version of the Ginsburg—Sand s Theorem and CAC\, when viewed as problems\, are Weihrauch equivalent.\n\ nI will present some new progress that has been made on this question. Thi s progress involves developing several new combinatorial problems related to CAC and ADS\, one of which is Weihrauch equivalent to the weakened vers ion of the Ginsburg—Sands Theorem\, and showing a variety of Weihrauch a nd computable reducibilities between them.\n LOCATION:https://researchseminars.org/talk/OLS/177/ END:VEVENT END:VCALENDAR