We study Schauder equivalence relations, which are Borel equivalence relations induced by actions of Banach spaces with Schauder bases. Firstly, we show that and are minimal Schauder equivalence relations. Then, we prove that neither of them is Borel reducible to the quotient where T is the Tsirelson space. This implies that they cannot form a basis for the Schauder equivalence relations. In addition, we apply an argument of Farah to show that every basis for the Schauder equivalence relations, if such (...) exist, has to be of cardinality. (shrink)

In this paper, notions of ‐like and c0‐like equivalence relations are introduced. We characterize the positions of ‐like and c0‐like equivalence relations in the Borel reducibility hierarchy by comparing them with equivalence relations and.