It's a causative construction, and I believe the underlined is an adjective (I'm sure there are additional terms that can be applied to it, but I would start with adjective). CJ is much better at this than I am: I eagerly anticipate his response.
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RatiatumSorry to disagree with Philip, but it is in fact a past participle. In this case the "have + object + past participle" structure is used to mean "to experience an event or action" : having his eyes opened.No argument that it is a past participle. But past participles, as well as present participles, can be used as adjectives. That is how