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How can we build syntax trees for sentences with enumerations?

I have three sentences as examples:

S1: John, Mary, Paul, Alice and Bob eat a cake.

S2: I'm eating an apple, a pear, a cherry, a strawberry and a banana.

S3: I'm working, eating, drinking and sleeping every day.

I'm a beginner in generative grammar. I've learned a bit about X-Bar theory, and it seems to me that all the syntax trees are binary trees (no more than two children for each node). In this context, I couldn't find any way to arrange the terms of an enumeration in such a binary tree.

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X-bar theory does require all branching to be binary. So in this theory, coordination is often handled by saying the conjunction is actually the head, and it takes one conjunct as its specifier and the other as its complement. (Some additional machinery then has to be invoked to explain why two conjoined DPs act like a DP, when the head of the phrase is a conjunction.)

You can then have enumerations be as long as you want, by postulating some sort of conjunction between each pair of items:

syntax tree for example 2

Then all but the last one get elided, which explains why there's often a brief pause between elements in an enumeration. (Or, if you prefer, there's another conjunction that acts like "and" but is phonologically null. But then you have to explain why you usually need a single "and" at the end and can't use the null conjunction for the whole thing.)

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