CAN ANYONE PLEASE SOLVE THE The Large Cardinal Project
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In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least α such that α=ωα). The proposition that such cardinals exist cannot be proved in the most common axiomatization of set theory, namely ZFC, and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results. In other words, they can be seen, in Dana Scott's phrase, as quantifying the fact "that if you want more you have to assume more".
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The Large Cardinal Project
- It is a field of set theory.
- a large cardinal property is a certain kind of property of transfinite cardinal numbers.
- Most working set theorists believe that the large cardinal axioms that are currently being considered are consistent with ZFC.
- Steel and Laver proved from a very large cardinal, a theorem about a tower of finite left-distributive ( a(bc) = (ab)(ac) ) algebras.
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