query: Is there a set A s.t. $|\mathcal{P}(A)| = |\mathbb{N}|$?
positive_passages.docid: 42095
positive_passages.text: Existence in ZF of a set with countable power set
negative_passages.docid: 51134
negative_passages.text: If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
negative_passages.docid: 151295
negative_passages.text: Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
negative_passages.docid: 44497
negative_passages.text: Can we equip the power set $P$ of any set $S$ with a binary operation such that $P$ becomes a group (with some restrictions)?
negative_passages.docid: 95294
negative_passages.text: Dense subset of $C[0,1]$ which preserves rationals
negative_passages.docid: 157924
negative_passages.text: $\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
negative_passages.docid: 18334
negative_passages.text: Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
negative_passages.docid: 31710
negative_passages.text: Show that $\mathcal{J}=\{[a, a+1) \mid a \in \mathbb{R}\}$ generates the Borel set of $\mathbb{R}$
negative_passages.docid: 130998
negative_passages.text: Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
negative_passages.docid: 111723
negative_passages.text: Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
negative_passages.docid: 69838
negative_passages.text: Does a countably infinite power set exist?
negative_passages.docid: 81843
negative_passages.text: Sequences of sets property
negative_passages.docid: 21431
negative_passages.text: The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
negative_passages.docid: 113614
negative_passages.text: Approximating the density of $S\cap[a,b]$ using a Folner Sequence of $A$, where $S \subseteq A$?
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 17461
negative_passages.text: Show that a set is dense in $[-1,1]$
negative_passages.docid: 7112
negative_passages.text: Product of sets and supremum