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 present …

Assume you have some notion of proof complexity: for instance, at the basic level, the length of a proof, or the number of symbols used, take your pick (there are more involved mea …

Can one define some measure of progress towards a proof of a statement? I'm not sure if it's even possible for general first order logic statements so let's restrict ourselves to p …

The Completeness Theorem in first-order logic states that any mathematical validity is derivable from axioms. Hence, any informal mathematical proof (which is rigorous) can be tran …

Why ZFC is placed in top of the proof system hierarchy? How it can p-simulate other systems?

Is there an oracle such that in the relativized world, bd-Frege (bounded depth Frege propositional proof system) has FIP (feasible interpolation property) but Frege does not hav …