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Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics

2008
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Bulletin of Symbolic Logic
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The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtained in suitable large cardinals properties. The first example I will treat is the proof that the

doi:10.2178/bsl/1208358846
fatcat:dw2rmhz54reldbz3dlznzghv44