Isomorphisms of trees

Abstract:

Let $\kappa$, $\lambda$ be cardinals, $\kappa \geq {\aleph _1}$ and regular, and $2 \leq \lambda \leq \kappa$. If $\kappa > {\aleph _1}$ and $\lambda < \kappa$, and if there is a $\kappa$-Suslin ($\kappa$-Aronszajn, $\kappa$-Kurepa) tree, then there are ${2^\kappa }$ normal $\lambda$-ary rigid nonisomorphic $\kappa$-Suslin ($\kappa$-Aronszajn, $\kappa$-Kurepa) trees. If there is a Suslin (Aronszajn, Kurepa) tree, then there is a normal rigid Suslin (Aronszajn, Kurepa) tree. If there is a $\kappa$-Canadian tree, then there are ${2^\kappa }$ normal $\lambda$-ary rigid nonisomorphic $\kappa$-Canadian trees.