query: Does the set of all finite sets exist according to ZFC?
positive_passages.docid: 156233
positive_passages.text: Why does the set of all singleton sets not exist?
negative_passages.docid: 104550
negative_passages.text: Countable union of countable sets(ZF)
negative_passages.docid: 144899
negative_passages.text: Do We Need the Axiom of Choice for Finite Sets?
negative_passages.docid: 91237
negative_passages.text: Every infinite set contains a countable subset
negative_passages.docid: 45792
negative_passages.text: Rigorous proof that surjectivity implies injectivity for finite sets
negative_passages.docid: 28452
negative_passages.text: Statement that is provable in $ZFC+CH$ yet unprovable in $ZFC+\lnot CH$
negative_passages.docid: 9082
negative_passages.text: Do sets, whose power sets have the same cardinality, have the same cardinality?
negative_passages.docid: 125683
negative_passages.text: Power set of a finite set is finite proof, no cardinality of power set
negative_passages.docid: 127200
negative_passages.text: Are there fields and ordered fields of every infinite cardinality?
negative_passages.docid: 70143
negative_passages.text: Mutually exclusive countable subsets of a countable set
negative_passages.docid: 117561
negative_passages.text: A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
negative_passages.docid: 2287
negative_passages.text: If a set is linearly independent, a finite subset of that set is also linearly independent
negative_passages.docid: 35692
negative_passages.text: The set of all finite subsets of the natural numbers is countable
negative_passages.docid: 147013
negative_passages.text: Subset of a finite set is finite
negative_passages.docid: 149926
negative_passages.text: ZFC with class terms: is any set also a class?
negative_passages.docid: 156252
negative_passages.text: Are sets constructed using only ZF measurable using ZFC?
negative_passages.docid: 78290
negative_passages.text: Countable axiom of choice: why you can't prove it from just ZF