Prove the existence of $X \subset \mathcal{P}(\mathbb{N})$ with continuum cardinality, such that each intersection of two of its elements is finite.
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
99464
Proof Concerning Indexed family of Sets and Intervals
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$
139078
Infinite partition of $\mathbb N$ by infinite subsets
66398
Union of a finite set and a countably infinite set is countably infinite
122947
What is the cardinality of the set of infinite cardinalities?
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
106455
intersection of infinite collection of finite sets?
102972
Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument
78117
Closed property of nonempty finite set
272
Cantor Sets/nonempty/cardinality
113922
Proof that the intersection of any finite number of convex sets is a convex set
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
66301
The cardinality of the set of countably infinite subsets of an infinite set
72190
Topological proof on discrete topology where $X$ is infinite
92249
Every finite set contains its supremum: proof improvement.