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I would need a hint for Exercise 23.10 of Jech's Set Theory (third edition), which states:

If $\kappa$ is a regular cardinal, then there exists a strongly almost disjoint family $\{X_\xi:\xi<\kappa^+\}$ of subsets of $\kappa$.

This means that each $X_\xi\subset \kappa$ is unbounded and for every $\theta<\kappa^+$ there exists ordinals $\delta_\xi<\kappa$ such that the sets $X_\xi\setminus \delta_\xi$, for $\xi<\theta$ are pairwise disjoint.

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This is same as almost disjoint. Suppose $\{X_{\xi} : \xi < \kappa^+\}$ is an almost disjoint family (so each $X_{\xi}$ is unbounded and any two of them meet on a bounded subset of $\kappa$). Given any $\kappa < \theta < \kappa^+$, list $\{X_{\xi} : \xi < \theta\}$ in order type $\kappa$ as $\{X_{\xi_i} : i < \kappa\}$ and inductively choose $\delta_{i} < \kappa$ such that $X_{\xi_i} \backslash \delta_i$ is disjoint with $X_{\xi_j}$ for every $j < i$. Now check.

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