Interval exchange transformation: Difference between revisions

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In [[computability theory]] a '''cylindric numbering''' is a special kind of [[numbering (computability theory)|numbering]] first introduced by [[Yuri L. Ershov]] in 1973.  
 
If a numberings <math>\nu</math> is [[reducibility (numbering)|reducible]] to <math>\mu</math> then there exists a computable function <math>f</math> with <math>\nu = \mu \circ f</math>. Usually <math>f</math> is not [[injective]] but if <math>\mu</math> is a cylindric numbering we can always find an injective <math>f</math>.  
 
== Definition ==
 
A numbering <math>\nu</math> is called '''cylindric''' if
:<math>\nu \equiv_1 c(\nu).</math>
That is if it is [[one equivalent numbering|one-equivalent]] to its [[cylindrification]]
 
A set <math>S</math> is called '''cylindric''' if its [[indicator function]]
:<math>1_S: \mathbb{N} \to \{0,1\}</math>
is a cylindric numbering.
 
== Examples ==
 
* every [[Gödel numbering]] is cylindric
 
== Properties ==
 
* cylindric numberings are [[idempotent]], <math>\nu \circ \nu = \nu</math>
 
== References ==
 
* Yu. L. Ershov, "Theorie der Numerierungen I." Zeitschrift für mathematische Logik und Grundlagen der Mathematik '''19''', 289-388 (1973).
 
[[Category:Theory of computation]]

Latest revision as of 02:25, 15 September 2014

Myrtle Benny is how I'm called and I really feel comfortable when people use the complete name. Body building is 1 of the issues I love most. Minnesota has always been his home but his spouse wants them to move. Managing people is what I do and the wage has been really fulfilling.

Feel free to visit my website :: http://geekyplasta.com/blogs/post/3926

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