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I'm assuming a finite alphabet and a finitely axiomatizable proof system per convention. I can't think of an uncountable set of propositions in which each can b
by gradschool 2mo ago
I'm assuming a finite alphabet and a finitely axiomatizable proof system per convention. I can't think of an uncountable set of propositions in which each can be written as a finite string of symbols, so that's what I was missing. Thank you for clearing this up for me.
- Xmd5a 2mo agoIf you substitute uncountability in your intuition with algorithmic incompressibility (too much information to be captured by shorter descriptions) you have Chaitin's incompleteness theorem. Kudos for the well-placed hunch!