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Results tagged with proof-theory
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user 12978
For question in Proof Theory, where "proofs" themselves are the object of mathematical investigation. It is not to be used to request a proof of some result.
4
votes
Accepted
Positive & Negative Arity
While I have never seen this notion before (it may be common or this may be the first paper that uses those terms), Comment 1 basically explains the idea. A relation $r$ in $\mathcal{R}_{n,m}$ is an …
- 6,287
10
votes
Proofs of Gödel's theorem
In a recent AMS notices article, Shira Kritchman and Ran Raz give a proof of Godel's Second Incompleteness Theorem based on the Surprise Examination Paradox.
- 6,287
4
votes
Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prer...
As for your question on prerequisites, the more logic you know the better. Of course the basic concepts---proofs, models, Peano arithmetic, incompleteness, compactness, nonstandard models, primitive …
3
votes
Algorithmic complexity of formal proof verification?
Given that I can cherry-pick the system, consider HOL Light. In HOL light (and probably in other systems like Isabelle and Coq), the proofs are written in a functional programming language (for HOL L …
- 6,287
8
votes
7
answers
648
views
Strength of Bishop style constructive mathematics vs $\mathsf{RCA}_0$
This question came out of this other MO question of mine. My question is
Is there a formal comparison between $\mathsf{RCA}_0$ and $\mathsf{BISH}$ (Bishop style constructive mathematics as used in c …
- 6,287
6
votes
Does formalizing math require search and creativity, or is it near-mechanical?
Like Henry, I am not an expert---although I've played around with formal proof assistants.
First, one has to take into account if the background material is already formalized. This can make a big …