Boolean-valued model

<p>In <a href="/facts/Mathematical_logic/SaI7Y3wN">mathematical logic</a>, a Boolean-valued model is a generalization of the ordinary <a href="/facts/Alfred_Tarski/7h6NySAj">Tarskian</a> notion of <a href="/facts/Structure_(mathematical_logic)/GsMx1fEb">structure</a> from <a href="/facts/Model_theory/vLWVV8sQ">model theory</a>. In a Boolean-valued model, the <a href="/facts/Truth_value/SY4e2w8l">truth values</a> of <a href="/facts/Proposition/0877MFMD">propositions</a> are not limited to "true" and "false", but instead take values in some fixed <a href="/facts/Complete_Boolean_algebra/7gtfjVjp">complete Boolean algebra</a>.
</p><p>Boolean-valued models were introduced by <a href="/facts/Dana_Scott/XEVddlVg">Dana Scott</a>, <a href="/facts/Robert_M._Solovay/75zxRfT4">Robert M. Solovay</a>, and <a href="/facts/Petr_Vop%25C4%259Bnka/SkeXTBf3">Petr Vopěnka</a> in the 1960s in order to help understand <a href="/facts/Paul_Cohen_(mathematician)/wMLaE3Vz">Paul Cohen</a>'s method of <a href="/facts/Forcing_(mathematics)/3vMqqKcq">forcing</a>. They are also related to <a href="/facts/Heyting_algebra/Rrny2LRq">Heyting algebra</a> semantics in <a href="/facts/Intuitionistic_logic/zI7ulCnM">intuitionistic logic</a>.
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Boolean-valued model open-in-new

Boolean-valued model