query: Replacing axiom of infinity
positive_passages.docid: 153935
positive_passages.text: A weaker Axiom of Infinity?
negative_passages.docid: 138897
negative_passages.text: help with some Hilbert style proofs in a propositional logic axiom system.
negative_passages.docid: 100333
negative_passages.text: Show A is countable infinity
negative_passages.docid: 115675
negative_passages.text: Strange consequences of Axiom of Choice in Zermelo set theory
negative_passages.docid: 34045
negative_passages.text: 3 Statements of axiom of choice are equivalent
negative_passages.docid: 65473
negative_passages.text: How can something finite become infinite?
negative_passages.docid: 137564
negative_passages.text: What exactly is meant by infinity?
negative_passages.docid: 35123
negative_passages.text: How do the separation axioms follow from the replacement axioms?
negative_passages.docid: 5313
negative_passages.text: Existence of how many sets is asserted by the axiom of choice in this case?
negative_passages.docid: 21202
negative_passages.text: Axiom of choice is equivalent to every relation includes a function with the same domain
negative_passages.docid: 140868
negative_passages.text: Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
negative_passages.docid: 83757
negative_passages.text: Is the following equivalent to the axiom of choice?
negative_passages.docid: 121060
negative_passages.text: ¿Can you help me with axiom of regularity?
negative_passages.docid: 49220
negative_passages.text: Open Sets of $\mathbb{R}^1$ and axiom of choice
negative_passages.docid: 149853
negative_passages.text: What infinity is greater than the continuum? Show with an example
negative_passages.docid: 22423
negative_passages.text: Which infinity is meant in limits?
negative_passages.docid: 29755
negative_passages.text: Power set equivalency of Axiom of Choice