Abstract
The purpose of this note is to survey some technical aspects of the two hypotheses c = ℵ1 and c = ℵ2 together with their joint negation c > ℵ2. The reader is probably already puzzled by the fact that we decide to stop at the second uncountable cardinal rather than at some other value of the aleph— function. Well, there are two reasons for this. The first one is that presently there is a considerable lack of knowledge about statements like c; = ℵ3, c = ℵ4, and so on. The other reason is that the present knowledge seems to suggest that indeed there is some “affinity” between c; and ℵ2. It also seems that even a meager understanding of this affinity can be quite useful as we shall demonstrate this at the end of the article.
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Todorčević, S. (1997). Comparing the Continuum with the First Two Uncountable Cardinals. In: Dalla Chiara, M.L., Doets, K., Mundici, D., van Benthem, J. (eds) Logic and Scientific Methods. Synthese Library, vol 259. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0487-8_8
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