Much needed terminology, that isn’t going to happen any time soon

One of the reasons I love set theory so much, and specifically choice related research, is that this is an extremely fertile ground for amusing terminology. We have forcing, cardinals, collapsing, we have all sort of gems and rodents at our disposal… we even have a swamp thing.

Here are a few terminological ideas that I doubt are going to be developed by anyone. But if you plan on doing something similar (or if my terminology inspires some proof) feel free to use these terms, and please let me know!

  1. Right of the bat, Gygaxian set theory, a dungeon and a dragon. Dungeon should be something which is related to forcing, perhaps some morass-like construction. It works very well if the construction involves lottery sums, many of which are trivial or semi-trivial. Then you can say that you roll the dice (by picking a generic) and slowly fight to kill the dragon, or carry your quest to find the dragon, or something. Who wouldn’t read a paper titled “Set Theoretic Dungeons and Dragons: A hero’s quest for the generic set”
  2. Zero nuke, $0^{\clubsuit}$ (the club suit looks a bit like a mushroom cloud). I know, I know, it’s a good thing that we’re moving on from the whole “dagger-pistol” terminology. But I can’t help and feel that a zero-nuke which is the mother-of-all sharps (MOAS?) is something worth defining. Perhaps something akin to the failure of the HOD conjecture.
  3. Genes. I don’t know what they might be, but they should be something that can be recombined, preferably in the context of forcing, and have different generics with different properties. Then by iterating gene recombination sequences you generate a lot of mutated structures. This might also be a good thing in the context of morass-like structures, with the genes being some particular property of the structure that we would like to “mutate” via a generic set. You also get a generic genetic recombination, for free!

I have plenty of other ideas, but I keep forgetting them. It’s good to let the silliness out from time to time. Feel free to ventilate your silly bones in the comments, or suggest improvements or other definitions for the terms I’ve given here.