Submitted by Benedetto Intrigila
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 -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.