In this paper we introduce some fusion properties of forcing notions which guarantee that an iteration with supports of size ▫$\le \kappa$▫ not only does not collapse ▫$\kappa^+$▫ but also preserves ...the strength of ▫$\kappa$▫ (after a suitable preparatory forcing). This provides a general theory covering the known cases of tree iterations which preserve large cardinals.
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