Do we know under which conditions the Kunen tree (Recall the Kunen tree provides an analysis of the equivalence classes of functions $f: \omega_1 \mapsto to \omega_1$ with respect to the normal measure $W^1_1$ on $\omega_1$) \omega_1$ under $AD$) is homogeneous, if it is? Do we know if and under which hypothesis the Martin tree (it is a generalization of the Kunen tree to all the projective hierarchy) is homogeneous? Any reference treating their homogeneity will be appreciated. Thx.
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Kunen tree and Martin treeDo we know under which conditions the Kunen tree (Recall the Kunen tree provides an analysis of the equivalence classes of functions $f: \omega_1 \mapsto \omega_1$ with respect to the normal measure $W^1_1$ on $\omega_1$) is homogeneous, if it is? Do we know if and under which hypothesis the Martin tree (it is a generalization of the Kunen tree to all the projective hierarchy) is homogeneous? Any reference treating their homogeneity will be appreciated. Thx.
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