query: Axiomatization of Natural Numbers that leads to a unique model
positive_passages.docid: 16534
positive_passages.text: Can $(\Bbb N,\leq)$ have an $\aleph_0$-categorical theory (in a larger language)?
negative_passages.docid: 126870
negative_passages.text: Show that axiom of replacement implies from the Axiom of Specification [Proof Verification]
negative_passages.docid: 43044
negative_passages.text: All natural numbers are equal.
negative_passages.docid: 32081
negative_passages.text: The dual version of trichotomy of cardinality without AC
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 52451
negative_passages.text: Ordered Triples and Set Theory
negative_passages.docid: 158671
negative_passages.text: Cardinality of a set that consists of all existing cardinalities
negative_passages.docid: 144592
negative_passages.text: how to prove the existence and uniqueness of the prime factorization of any natural number.
negative_passages.docid: 141299
negative_passages.text: Alternative set theories
negative_passages.docid: 83757
negative_passages.text: Is the following equivalent to the axiom of choice?
negative_passages.docid: 135025
negative_passages.text: Axiomatization of a Topology using the Boundary
negative_passages.docid: 85398
negative_passages.text: $\mathsf{ZF}$ is not finitely axiomatizable
negative_passages.docid: 43503
negative_passages.text: Bases of complex vector spaces and the axiom of choice
negative_passages.docid: 70439
negative_passages.text: Mapping two integers to one, in a unique and deterministic way
negative_passages.docid: 67490
negative_passages.text: Restricing domains for universal and existential quantifiers
negative_passages.docid: 126713
negative_passages.text: Strong induction and vacuous truth
negative_passages.docid: 94617
negative_passages.text: Showing Consistency and Completeness implies a unique truth assignment