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Results tagged with proof-theory
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user 50073
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.
7
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0
answers
234
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Unprovable integer identity involving exponentiation
I was thinking about Tarski's problem, and was wondering what happens if we have a theory $T$ with two sorts $N,Z$ with intended interpretations $\def\nn{\mathbb{N}}$$\def\zz{\mathbb{Z}}$$\nn,\zz$ res …
- 2,912
7
votes
1
answer
244
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Independent/Easy fraction of sentences over PA
Let $S(n)$ be the set of all sentences over PA of length at most $n$ (counting the quantifier symbols, boolean connectives, arithmetic operations and constants, and counting each variable as length $1 …
- 2,912
4
votes
0
answers
159
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Can this theory of dyadic rationals prove that multiplying by three is the same as summing t...
(This question arose from a discussion with Jade Vanadium about a theory of dyadic rationals.)
Let $T$ be the 2-sorted FOL theory with sorts $ℕ,ℚ$ and constant-symbols $0,1$ and binary function-symbol …
- 2,912
4
votes
1
answer
364
views
Does ACA prove categoricity of the reals?
$\def\f#1{\text{#1}}$Does $\f{ACA}$ prove that any two internally complete ordered fields are isomorphic?
Here internal completeness is expressed roughly as "every sequence of reals with an upper boun …
- 2,912