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Undecidability of Topologicaland Arithmetical Propertiesof Infinitary Rational Relations
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- Journal:
- RAIRO - Theoretical Informatics and Applications / Volume 37 / Issue 2 / April 2003
- Published online by Cambridge University Press:
- 15 November 2003, pp. 115-126
- Print publication:
- April 2003
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- Article
- Export citation
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We prove that for every countable ordinal α one cannot decidewhether a given infinitary rational relation is in the Borel class ${\bf \Sigma_{\alpha}^0}$
(respectively ${\bf \Pi_{\alpha}^0}$ 
). Furthermoreone cannotdecide whether a given infinitary rational relation is a Borel set or a ${\bf \Sigma_{1}^1}$ 
-complete set. We prove some recursive analogues to theseproperties. In particular one cannot decide whether an infinitary rational relation is anarithmetical set.We then deduce from the proof ofthese results some other ones, like: one cannot decide whether thecomplement ofan infinitary rational relation is also an infinitary rational relation.
On the Topological Complexity of Infinitary Rational Relations
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- Journal:
- RAIRO - Theoretical Informatics and Applications / Volume 37 / Issue 2 / April 2003
- Published online by Cambridge University Press:
- 15 November 2003, pp. 105-113
- Print publication:
- April 2003
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- Article
- Export citation
