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Amoeba relation and Galois-Tukey connections. (English) Zbl 0824.03026
We continue the research from our earlier paper “Generalized Galois- Tukey connections between explicit relations on classical objects of real analysis” [Israel Math. Conf. Proc. 6, 619-643 (1993)]. We introduce a new (internal) structure related with the amoeba forcing (in contrast with external structures related with generic objects) and we show that it is equivalent to the inclusion restricted to measure zero sets. Finally, we complete results adding some extremal relations in the Galois-Tukey lattice of binary relations.
MSC:
03E35 Consistency and independence results
03E05 Other combinatorial set theory
26A21 Classification of real functions; Baire classification of sets and functions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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