query: Ordinals that are not cardinals
positive_passages.docid: 157187
positive_passages.text: Why $\omega+1$ and $\omega^2$ are not cardinal numbers?
negative_passages.docid: 25685
negative_passages.text: What is the product of all nonzero, finite cardinals?
negative_passages.docid: 6210
negative_passages.text: Countable compact spaces as ordinals
negative_passages.docid: 19414
negative_passages.text: Uncountable subset with uncountable complement, without the Axiom of Choice
negative_passages.docid: 32081
negative_passages.text: The dual version of trichotomy of cardinality without AC
negative_passages.docid: 132537
negative_passages.text: Class of sets of a given infinite cardinality
negative_passages.docid: 30587
negative_passages.text: Uncountable well ordered set in $Z^-$ theory.
negative_passages.docid: 34972
negative_passages.text: order of non abelian group can't be what?
negative_passages.docid: 112008
negative_passages.text: Ordinal $\omega_1$ is not compact
negative_passages.docid: 38726
negative_passages.text: What set theory axioms do I need to believe in uncountable ordinals?
negative_passages.docid: 45878
negative_passages.text: Elementary Set Theory: Ordinals, Well Orderings and Isomorphisms
negative_passages.docid: 3135
negative_passages.text: Is a limit ordinal necessarily a cardinal?
negative_passages.docid: 70369
negative_passages.text: Why do we use von Neumann ordinals and not Zermelo ordinals?
negative_passages.docid: 88099
negative_passages.text: Not $\sigma$-compact set without axiom of choice
negative_passages.docid: 39129
negative_passages.text: Simplest Example of a Poset that is not a Lattice
negative_passages.docid: 16971
negative_passages.text: Prove that no ordinal is an element of itself
negative_passages.docid: 150719
negative_passages.text: All nonisomorphic trees of order $n$