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Vladimir Kanovei

Note that Hausdorff defined his $\eta_\alpha$ fields differently, as "pantachies", that is, linearly ordered subsets of a certain partial order of R^N, and with a heavy dose of the axiom of choice - which does not yeild any single, well-defined, concrete example. Thus the countably saturated rcof which emerges as a certain initial part of No is probably the closest thing to the notoriously inconsistent "infinitaire pantachie" of DuBoisReymond known so far.

Note that Hausdorff studied his $\eta_\alpha$ fields most successfully as "pantachies", that is, linearly ordered subsets of a certain partial order of R^N, and with a heavy dose of the axiom of choice - which does not yeild any single, well-defined, concrete example. Thus the countably saturated rcof which emerges as a certain initial part of No is probably the closest thing to the notoriously inconsistent "infinitaire pantachie" of DuBoisReymond known so far.