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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].


The question is how many fixed points can a combinator (i.e. a closed term) have in the λβ  -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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