Does there exist an uncountably large set of sets of natural numbers $S$ such that, for all pairs of elements in $S$, one is a subset of the other?

Asked Dec 20 '23 at 02:15

Active Dec 20 '23 at 03:15

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Does there exist an uncountably large set of sets of natural numbers $S$ such that, for all pairs of elements in $S$, one is a subset of the other? For example, there’s $\{\{\},\{1\},\{1,2\},\{1,2,3\},\ldots\}$ which has the property, but is only countably large.

edited Dec 20 '23 at 03:15

Sassatelli Giulio

asked Dec 20 '23 at 02:15

flakpm

Does there exist an uncountably large set of sets of natural numbers $S$ such that, for all pairs of elements in $S$, one is a subset of the other?

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