Answer by Henry Towsner for Notable examples of syntactic proofs whose...
There's a good reason that concrete examples are going to be rare. Existence of a first-order proof (at least in a countable language) is a $\Sigma_1$ property in the language of arithmetic, and it's a...
View ArticleAnswer by user44143 for Notable examples of syntactic proofs whose existence...
George Boolos has a nice example in "A Curious Inference", where $\mathbb{T}\vDash\sigma$ is obvious from second-order or semantic considerations, but $\mathbb{T}\vdash\sigma$ is of Ackermann...
View ArticleAnswer by godelian for Notable examples of syntactic proofs whose existence...
If you are willing to consider completeness of fragments of first-order logic, one example that would follow under your scheme is the conservativity of classical logic over its fragment of coherent...
View ArticleNotable examples of syntactic proofs whose existence is guaranteed by...
Question.What are examples (preferably documented and explicitly commented on from this perspective in the literature, preferably in an article dedicated to this aspect alone) of the following...
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