Abstract
In his fascinating book “To Mock a Mockingbird”, Ray Smullyan asks whether a fixed point combinator can be constructed from the Bluebird B, the Identity Bird I, and the Mockingbird M (sometimes called “little omega”). This is still not known.The mockingbird is only a special kind of mimid. Mimids are those birds which upon hearing the name of x, say what x would say upon hearing the name of some other y. In this note we shall characterize the set of mimids that occur in the Bluebird/Mockingbird flock.
For Ray Smullyan:
Hush, little baby, don’t say a word,
Raymond’s gonna buy you a mockingbird.
If that mockingbird won’t mock,
Raymond’s gonna buy you some Google stock!
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References
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Statman, R. (2017). Some Tweets About Mockingbirds. In: Fitting, M., Rayman, B. (eds) Raymond Smullyan on Self Reference. Outstanding Contributions to Logic, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-68732-2_6
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DOI: https://doi.org/10.1007/978-3-319-68732-2_6
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