axiom schema of replacement
in set theory, the axiom schema that the image of a set under a definable class function is also a set
| rdfs:label |
"axiom schema of replacement"@en
|
|
skos:alt |
"axiom schema of collection"@en
|
| schema:description |
"in set theory, the axiom schema that the image of a set under a definable class function is also a set"@en
|
|
schema:date |
"2026-09-06T17:40:40+00:00"^^xsd:dateTime |
| schema:version | 2541223524 |
| wikibase:identifiers | 8 |
| wikibase:sitelinks | 17 |
| wikibase:statements | 17 |
| p:P12888 | wd:statement/Q1361825-2497c6b2-4da6-d493-97c9-09340f4d94d3 |
| p:P1417 | wd:statement/Q1361825-9054D7AD-BF4D-47CA-A5E0-7E874067DD5E |
| p:P2534 | wd:statement/Q1361825-CB800C2F-335D-41B8-B686-79DC9DFC5D26 |
| p:P2579 | wd:statement/Q1361825-28f9ee24-42e7-2850-0cce-9af2c0f30ede |
| p:P279 | wd:statement/Q1361825-851bc68b-4765-206f-6a41-76dacae779f4 |
| p:P2812 | wd:statement/Q1361825-c48ea1e8-44a3-3b46-8ac5-bbc6cc046bdc |
| p:P31 | wd:statement/Q1361825-3d6b7277-459e-ce12-63a0-fc4eca92ffb7 |
| p:P3417 | wd:statement/Q1361825-7AAF422B-D1C0-464E-AC7F-AEDA2CBFD303 |
| p:P361 | wd:statement/Q1361825-36B3AC3A-47B4-4D14-B909-8152D221D4E6 |
| p:P4215 | wd:statement/Q1361825-bbed9db6-4123-5f2a-c57e-f808a1ace0a5 |
| p:P5555 | wd:statement/Q1361825-acaab855-4632-aa58-563b-86cebd2e8af5 |
| p:P575 | wd:statement/Q1361825-3153dd55-4493-dc2c-61c9-8c039a0965c6 |
| p:P61 | wd:statement/Q1361825-20af50e0-497b-c0b1-d5ef-32922e29a854 |
| p:P6104 | wd:statement/Q1361825-72D1790F-0902-4DA6-9538-E7F403951CCD |
| p:P6366 | wd:statement/Q1361825-4D4A9DEC-6055-46F8-9754-AF8ACB946323 |
| p:P646 | wd:statement/Q1361825-95B8BABA-6D4E-417B-8039-F4900678D878 |
| p:P6781 | wd:statement/Q1361825-7f2b1dd6-4edf-238b-1dc3-6dc6fbe01bfa |
|
p:direct- |
<https:/ |
| wdt:P12888 | "ax-rep" |
| wdt:P1417 | "topic/axiom-schema-of-replacement" |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">∀</mi><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mspace width="0.167em"></mspace><mi mathvariant="normal">∀</mi><mi>A</mi><mspace width="0.167em"></mspace><mi mathvariant="normal">∃</mi><mi>B</mi><mspace width="0.167em"></mspace><mi mathvariant="normal">∀</mi><mi>x</mi><mspace width="0.167em"></mspace><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>B</mi><mo stretchy="false">⇔</mo><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>A</mi><mo stretchy="false">∧</mo><mi>φ</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo>,</mo><mi>A</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | Zermelo–Fraenkel set theory |
| wdt:P279 | axiom |
| wdt:P2812 | "AxiomofReplacement" |
| wdt:P31 | axiom schema |
| wdt:P3417 | "Axiom-Schema-of-Replacement" |
| wdt:P361 | list of axioms |
| wdt:P4215 | "axiom of replacement" |
| wdt:P5555 |
<http:/ |
| wdt:P575 | "1921-01-01T00:00:00+00:00"^^xsd:dateTime |
| wdt:P61 | Abraham Fraenkel |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "2780877781" |
| wdt:P646 | "/m/0ds27" |
| wdt:P6781 | "Axiom:Axiom_of_Replacement" |
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