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(PDF) Avoiding Self-Referential Statements
Recursion-theoretic proofs of metamathematical results tend to rely on a pair of effectively inseparable r.e. sets and its properties. We establish a special property for a small configuration of such pairs and derive from it some…
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Ordinal analysis - Wikipedia
If theories have the same proof-theoretic ordinal they are often equiconsistent, and if one theory has a larger proof-theoretic ordinal than another it can often prove the consistency of the second theory.
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Constructive Mathematics (Stanford Encyclopedia of Philosophy)
It should, by now, be clear that a full-blooded computational development of mathematics disallows the idealistic interpretations of disjunction and existence upon which most classical mathematics depends.
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Proof theory of IDs 8.09
The proof theory of classical and constructive inductive definitions.
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Mathematical Freedom, Truth, and Coherence
I present a novel account of mathematical truth, drawing on the doctrine of alethic pluralism, according to which (to a first approximation) mathematical truth is realized by the property of coherence.
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The following paper was originally published
Peter W. Osel, Siemens Components, Inc.
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The proof-theoretic strength of Ramsey’s theorem for pairs
Ludovic Patey1 and Keita Yokoyama2
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