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the claim
The axiom of infinity is logically independent of the other Zermelo-Fraenkel axioms.
the verdict
SUPPORTED
the evidence backs this
refutedsupported
the weight of evidence
1 source for · 0 against
AS REPORTEDno primary record reached; this is what the reporting says

Retrieved literature confirms that the axiom of infinity is independent of the other axioms of set theory, assuming consistency.

Evidence for · 1
Some proofs of independence in axiomatic set theory 1
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Some proofs of independence in axiomatic set theory1 | The Journal of Symbolic Logic | Cambridge Core Search --- Institution Login Search Hostname: page-component-6565fbc58-595z8 Total loading time: 0 Render date: 2026-03-12T02:57:28.009Z Has data issue: false hasContentIssue false - Français - English # Some proofs of independence in axiomatic set theory1 Published online by Cambridge University Press: 12 March 2014 Elliott Mendelson Show author details --- --- Article contents - References - Footnotes - Extract Get access Share Cite Rights & Permissions --- ## Extract 1. Gödel's theorem that sufficiently strong formal systems cannot prove their own consistency and Tarski's method for constructing truth-definitions can be combined to give several independence results in axiomatic set theory. In substance, the following theorems can be obtained: (a) The existence of inaccessible ordinals is not provable from the axioms of set theory, if these axioms are consistent, (b) The axiom of infinity is independent of the other axioms, if these other axioms are consistent, (c) The axiom of replacement is independent of the other axioms, if these other axioms are consisten
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The analysis

rails:sufficiency:supported:single_source:for=1+0p:against=0+0p | v55:sufficiency

Everything we examined (1)
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  1. Some proofs of independence in axiomatic set theory 1referenceno side taken
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first checked04 Aug 2026
judged → INSUFFICIENT EVIDENCE · 004 Aug 2026
held for human review08 Aug 2026
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