Lexical subarray

Chomsky (1998) proposes to divide lexical arrays into lexical subarrays because of the grammaticality of sentences like (i):

(i) There is a possibility that [A a proof
    will be discovered ]

Suppose that the words in (i) are all in the same lexical array: Merge-over-Move favors merger of there over movement of a proof at stage A in the derivation, so (i) can't be derived, and we can only derive (ii):

(ii) A possibility is that there will be discovered
     a proof.

The problem disappears if we divide the lexical array for (i) into two subarrays: one for the embedded clause (not containing there) and one for the matrix clause (containing there). (ii) can be derived by doing the opposite: selecting a subarray with an expletive for the embedded clause, and a subarray without an expletive for the matrix clause.
Chomsky proposes to determine lexical subarrays on interpretational grounds, as 'the closest syntactic counterpart to a proposition', vP or CP. So a lexical subarray must contain a v or a C, and as many arguments as necessary to satisfy the selectional requirements of v/C.
The syntactic objects that are derived by choice of a subarray, are called phases.

Link

Utrecht Lexicon of Linguistics

References

• Chomsky, N. 1998. Minimalist inquiries: the framework, MIT working papers in linguistics.