query: the power set of every well-ordered set is well-ordered implies well ordering
positive_passages.docid: 42314
positive_passages.text: Without appealing to choice, can we prove that if $X$ is well-orderable, then so too is $2^X$?
negative_passages.docid: 36789
negative_passages.text: The power set of the intersection of two sets equals the intersection of the power sets of each set
negative_passages.docid: 72104
negative_passages.text: Totally ordering the power set of a well ordered set.
negative_passages.docid: 125683
negative_passages.text: Power set of a finite set is finite proof, no cardinality of power set
negative_passages.docid: 30587
negative_passages.text: Uncountable well ordered set in $Z^-$ theory.
negative_passages.docid: 127200
negative_passages.text: Are there fields and ordered fields of every infinite cardinality?
negative_passages.docid: 120522
negative_passages.text: Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
negative_passages.docid: 7214
negative_passages.text: Does linear ordering need the Axiom of Choice?
negative_passages.docid: 6113
negative_passages.text: Proof of Strong principle of Induction (T. Tao Analysis I)
negative_passages.docid: 72371
negative_passages.text: Proof of Strong Induction Using Well-Ordering Principle
negative_passages.docid: 156335
negative_passages.text: Proving Power Set of $\mathbb N$ is Uncountable
negative_passages.docid: 79974
negative_passages.text: The cardinality of Lebesgue sets
negative_passages.docid: 70196
negative_passages.text: Is there any well-ordered uncountable set of real numbers under the original ordering?
negative_passages.docid: 92249
negative_passages.text: Every finite set contains its supremum: proof improvement.
negative_passages.docid: 87830
negative_passages.text: Relating the union of the power set of a set to the set itself
negative_passages.docid: 45792
negative_passages.text: Rigorous proof that surjectivity implies injectivity for finite sets
negative_passages.docid: 68230
negative_passages.text: The cardinality of a countable union of sets with less than continuum cardinality