If a Fighter 3 (Eldritch Knight) levels up as a Warlock for the rest of the way to 20, making him an 18th level caster according to the multiclass spell slot table provided, would he in turn be able to learn 9th level spell? Meeting only the requirements listed for Warlock upon leveling, being 1 spell on it's list for which it has spell slots available for.
(Note: I would put up quotes and annotations providing source material but I'm running on limited time and my question sounds convoluted and simple to solve to the point where it's just me being dumb.)
Best Answer
I understand your question, but I'm afraid you've made a mistake in your calculations. An Eldrtich Knight 3/Warlock 17 does not have a caster level of 18 for the purposes of multiclass spellcasting. It has two separate kinds of casting: level 3 Eldritch Knight casting and level 17 Warlock casting. As it says on PHB 164:
Note that in the Spell Slots list, Warlock is not listed. You don't add together your EK and Warlock levels, because one gives you Pact Magic and the other gives you Spellcasting, which don't stack.
If you're an Eldritch Knight 3/Warlock 17, then you can cast EK spells using Warlock slots and Warlock spells using EK slots, but neither kinds of casting are improved by having the other class.