Aiōnios (αἰώνιος, Strong's g166) is the adjective behind almost every "eternal" and "everlasting" in the lake-of-fire texts. Rev 20:10 intensifies it further: the devil, beast, and false prophet are tormented eis tous aiōnas tōn aiōnōn, "unto the ages of the ages": the strongest durational phrase Greek has. Matt 25:46 puts "eternal punishment" and "eternal life" under that same single word in one sentence. Because one adjective covers both nouns in one breath, eternal-conscious-torment reads the verse as settling the question by grammar alone: a "punishment" that ends could not sit beside a "life" that does not.
Conditionalists press back at the word itself. Aiōnios is built on aiōn, "age," and in a handful of places it describes a state's outcome rather than an unending process: "eternal fire" already burned out over Sodom and Gomorrah (Jude 1:7), and Isa 66:24's undying worm and unquenched fire (echoed in Mark 9:48) picture a corpse-pit, not perpetual conscious pain. On this reading "eternal punishment" could mean punishment with an everlasting result (the second death is final and irreversible) rather than an everlasting process.
The traditional, majority reading stays with the durational sense: Rev 20:10's repeated, ongoing torment of the devil, beast, and false prophet across and beyond the millennium resists a one-time consuming fire. But the lexical steelman is real, honestly built, and it is the entire debate condensed into one Greek word.
For the book's wider argument, see the Revelation study guide.