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Some representations of Diophantine sets

Journal of Symbolic Logic, 1972
A set D of natural numbers is called Diophantine if it can be defined in the formwhere P is a polynomial with integer coefficients. Recently, Ju. V. Matijasevič [2], [3] has shown that all recursively enumerable sets are Diophantine. From this, it follows that a bound for n may be given.We use throughout the logical symbols ∧ (and), ∨ (or), → (if ...
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Quotient Sets and Diophantine Equations

The American Mathematical Monthly, 2011
Quotient sets 핌/핌 = {u/u′ : u, u′ ∊ 핌} have been considered several times before in the Monthly.
null Stephan Ramon Garcia +3 more
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Diophantine sets and algorithmic undecidability

1977
In §4 of Chapter V we showed that enumerable sets are the same thing as projections of level sets of primitive recursive functions. The projections of the level sets of a special kind of primitive recursive function—polynomials with coefficients in Z+—are called Diophantine sets.
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Diophantine approximation and Cantor sets

Mathematische Annalen, 2008
The irrationality exponent of a real number \(\xi\) is the supremum over all \(\mu\) for which the inequality \[ \left| \xi - {p \over q}\right| < {1 \over {q^\mu}} \] has infinitely many rational solutions \(p/q\). For any real irrational number \(\xi\) the irrationality exponent \(\mu(\xi)\) is at least \(2\).
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