Prove that an infinite recursively enumerable subset of natural numbers is the image of some injective...
$begingroup$
Let $X$ be an infinite recursively enumerable subset of natural numbers.
I want to show that $X$ is the image of some injective recursive function.
I was wondering how I can prove this question.
Is there a way I can prove this without using course-of-values recursion?
logic recursion
asked Dec 13 '18 at 19:59
astro_chaeastro_chae
63
$endgroup$
add a comment |
$begingroup$
Let $X$ be an infinite recursively enumerable subset of natural numbers.
I want to show that $X$ is the image of some injective recursive function.
I was wondering how I can prove this question.
Is there a way I can prove this without using course-of-values recursion?
logic recursion
asked Dec 13 '18 at 19:59
astro_chaeastro_chae
63
$endgroup$
$begingroup$
What model of computation are you using? Turing machines? Or $mu$-recursion? Or what?
$endgroup$
– Rob Arthan
Dec 13 '18 at 20:28
add a comment |
$begingroup$
Let $X$ be an infinite recursively enumerable subset of natural numbers.
I want to show that $X$ is the image of some injective recursive function.
I was wondering how I can prove this question.
Is there a way I can prove this without using course-of-values recursion?
logic recursion
asked Dec 13 '18 at 19:59
astro_chaeastro_chae
63
$endgroup$
Let $X$ be an infinite recursively enumerable subset of natural numbers.
I want to show that $X$ is the image of some injective recursive function.
I was wondering how I can prove this question.
Is there a way I can prove this without using course-of-values recursion?
logic recursion
logic recursion
asked Dec 13 '18 at 19:59
astro_chaeastro_chae
63
asked Dec 13 '18 at 19:59
astro_chaeastro_chae
63
edited Dec 13 '18 at 20:05
astro_chae
asked Dec 13 '18 at 19:59
astro_chaeastro_chae
63
asked Dec 13 '18 at 19:59
astro_chaeastro_chae
63
asked Dec 13 '18 at 19:59
astro_chaeastro_chae
63
63
$begingroup$
What model of computation are you using? Turing machines? Or $mu$-recursion? Or what?
$endgroup$
– Rob Arthan
Dec 13 '18 at 20:28
add a comment |
$begingroup$
What model of computation are you using? Turing machines? Or $mu$-recursion? Or what?
$endgroup$
– Rob Arthan
Dec 13 '18 at 20:28
$begingroup$
What model of computation are you using? Turing machines? Or $mu$-recursion? Or what?
$endgroup$
– Rob Arthan
Dec 13 '18 at 20:28
$begingroup$
What model of computation are you using? Turing machines? Or $mu$-recursion? Or what?
$endgroup$
– Rob Arthan
Dec 13 '18 at 20:28
add a comment |
0
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$begingroup$
What model of computation are you using? Turing machines? Or $mu$-recursion? Or what?
$endgroup$
– Rob Arthan
Dec 13 '18 at 20:28