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Apr
6
awarded  Yearling
Apr
3
comment Is the two variable fragment of arithmetic, i.e., theory of ($\mathbb{N}, + ,\times$), decidable?
Sorry, I should have asked "Is every sentence equivalent to a boolean combination of 2-quantifier formulas in prenex form?" Also, It would be helpful if you said what you mean by "the two variable fragment of arithmetic".
Apr
3
comment Is the two variable fragment of arithmetic, i.e., theory of ($\mathbb{N}, + ,\times$), decidable?
In "two-variable arithmetic" does every sentence have an equivalent prenex form consisting of an $x$-quantifier and a $y$-quantifier (in some order) followed by an open formula?
Jan
21
awarded  Good Answer
Dec
16
comment How Symmetric is Diophantine Approximation using Fractions with Square Denominators?
These can't be all of the best approximations, because they are all less than the Liouville number.
Dec
14
comment A question regarding a fragment of Robinson Arithmetic
In your language you can say that every element is even or odd. This is true in the non-negative integers under addition but false for the set of polynomials with non-negative leading coefficients (under addition, with successor defined in the obvious way.)
May
18
awarded  Nice Question
Apr
6
awarded  Yearling
Apr
3
revised divisible by all standard prime numbers
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Apr
2
revised divisible by all standard prime numbers
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Apr
2
revised divisible by all standard prime numbers
deleted 32 characters in body
Apr
2
revised divisible by all standard prime numbers
added 32 characters in body
Apr
2
answered divisible by all standard prime numbers
Jan
22
awarded  Enlightened
Jan
22
awarded  Nice Answer
Sep
10
awarded  Enlightened
Aug
27
comment Algorithm for determining when polynomial iteration is bounded?
@Per: Thank you for the reference to the result on IFS undecidability. Alas, I don't see how to the IFS result here. However the second point, about the map $x\to x-1/x$ seems really interesting. Do you have a reference?
Aug
26
asked Algorithm for determining when polynomial iteration is bounded?
Jul
2
awarded  Curious
Jun
14
awarded  Enlightened