@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-C1C1Z6ZF-X
  skos:definition """En théorie des ensembles, l'<b>axiome de Martin</b>, introduit par Donald A. Martin et Robert M. Solovay en 1970, est un énoncé indépendant de ZFC, l'axiomatique usuelle de la théorie des ensembles. C'est une conséquence de l'hypothèse du continu, mais l'axiome de Martin est également cohérent avec la négation de celle-ci. Informellement, l'axiome de Martin affirme que tous les cardinaux strictement inférieurs à <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle 2^{\\\\aleph _{0}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mn>2</mn>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <msub>
<br/>              <mi mathvariant="normal">ℵ<!-- ℵ --></mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>0</mn>
<br/>              </mrow>
<br/>            </msub>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle 2^{\\\\aleph _{0}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/779da5db4ed54fa334dd92089cdf1c284e45febb" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:3.231ex; height:2.676ex;" alt="2^{\\\\aleph _{0}}"></span> se comportent comme <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\aleph _{0}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi mathvariant="normal">ℵ<!-- ℵ --></mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\aleph _{0}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721cd7f8c15a2e72ad162bdfa5baea8eef98aab1" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.475ex; height:2.509ex;" alt="\\\\aleph_0"></span>. C'est une généralisation du lemme de Rasiowa-Sikorski&nbsp; 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Axiome_de_Martin">https://fr.wikipedia.org/wiki/Axiome_de_Martin</a>)"""@fr, """In the mathematical field of set theory, <b>Martin's axiom</b>, introduced by Donald A. Martin and Robert M. Solovay, is a statement that is independent of the usual axioms of ZFC set theory. It is implied by the continuum hypothesis, but it is consistent with ZFC and the negation of the continuum hypothesis. Informally, it says that all cardinals less than the cardinality of the continuum, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\\\mathfrak {c}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="fraktur">c</mi>
<br/>          </mrow>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\\\mathfrak {c}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21924b960341255be18e538e51404718f29cbc0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:0.905ex; height:1.676ex;" alt="{\\\\mathfrak {c}}"></span>, behave roughly like <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\aleph _{0}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi mathvariant="normal">ℵ<!-- ℵ --></mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\aleph _{0}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721cd7f8c15a2e72ad162bdfa5baea8eef98aab1" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.475ex; height:2.509ex;" alt="\\\\aleph _{0}"></span>. The intuition behind this can be understood by studying the proof of the Rasiowa–Sikorski lemma. It is a principle that is used to control certain forcing arguments. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Martin%27s_axiom">https://en.wikipedia.org/wiki/Martin%27s_axiom</a>)"""@en ;
  skos:prefLabel "axiome de Martin"@fr, "Martin's axiom"@en ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Martin%27s_axiom>, <https://fr.wikipedia.org/wiki/Axiome_de_Martin> ;
  dc:modified "2023-08-21"^^xsd:date ;
  skos:broader psr:-T88XBMNP-M ;
  dc:created "2023-08-21"^^xsd:date ;
  a skos:Concept .

psr:-T88XBMNP-M
  skos:prefLabel "set theory"@en, "théorie des ensembles"@fr ;
  a skos:Concept ;
  skos:narrower psr:-C1C1Z6ZF-X .