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#### Problem # 25

Submitted by Benedetto Intrigila

Date: 2000

Statement. How many ﬁxed points can a combinator have?

Problem Origin. First posed in [Intrigila and Biasone, 2000].

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The question is how many ﬁxed points can a combinator (i.e. a closed term)
have in the -calculus. In [Intrigila and Biasone, 2000] it is proved that, if
a combinator has a ﬁxed point in normal form then, it has either an inﬁnite
number of ﬁxed points or exactly one ﬁxed point.

##### References for # 25

[Intrigila and Biasone, 2000] Intrigila, B. and Biasone, E. (2000). On the
number of ﬁxed points of a combinator in lambda calculus. Mathematical
Structures in Computer Science, 10(5):595–615.

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Last modified: July 21, 2014