Axioms of determinacy and biorthogonal systems
- Cite this article as:
- Godefroy, G. & Louveau, A. Israel J. Math. (1989) 67: 109. doi:10.1007/BF02764903
If allΠn1 games are determined, every non-norm-separable subspaceX ofl∞(N) which is W* —Σn+1/1 contains a biorthogonal system of cardinality 2ℵ0. In Levy’s model of Set Theory, the same is true of every non-norm-separable subspace ofl∞(N) which is definable from reals and ordinals. Under any of the above assumptions,X has a quotient space which does not linearly embed into 1∞(N).