The truth about some Post numbers
Krister Segerberg · Journal of Symbolic Logic · 1976
There is a mistake in [6], discovered by Robert V. Kohn: contrary to the claim on p. 714, the set {◊Xi: i ≥ 2} is not independent in S3. As a result three problems thought to be settled are open once more, viz., whether the Post numbers of S2, S3, and K4 are denumerable. In [6] it was claimed they are not. Now we shall prove that that claim is indeed correct for S2 and K4 but, surprisingly enough, not for S3.