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modal auxiliary

noun
  1. Grammar. any of the group of English auxiliary verbs, including can, could, may, might, shall, should, will, would, and must, that are used with the base form of another verb to express distinctions of mood.
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Origin of modal auxiliary

First recorded in 1930–35
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018