The tag has no usage guidance.

learn more… | top users | synonyms

21
votes
13answers
2k views

Are there any good nonconstructive “existential metatheorems”?

Are there any good examples of theorems in reasonably expressive theories (like Peano arithmetic) for which it is substantially easier to prove (in a metatheory) that a proof exists than it is ...
58
votes
29answers
6k views

Can infinity shorten proofs a lot?

I've just been asked for a good example of a situation in maths where using infinity can greatly shorten an argument. The person who wants the example wants it as part of a presentation to the general ...
6
votes
2answers
867 views

“Requires axiom of choice” vs. “explicitly constructible”

I think I'm a bit confused about the relationship between some concepts in mathematical logic, namely constructions that require the axiom of choice and "explicit" results. For example, let's take ...