Appears in collections : 13th International workshop in set theory / 13ème Atelier international de théorie des ensembles, 13th International workshop in set theory / 13ème Atelier international de théorie des ensembles

In 1971 Baumgartner showed it is consistent that any two $\aleph_1$-dense subsets of the real line are order isomorphic. This was important both for the methods of the proof and for consequences of the result. We introduce methods that lead to an analogous result for $\aleph_2$-dense sets.

Keywords : forcing - large cardinals - Baumgartner isomorphism - infinitary Ramsey principles - reflection principles