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Documents  Fontanella, Laura | enregistrements trouvés : 2

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Logic and Foundations

We discuss classical realizability, a branch of mathematical logic that investigates the computational content of mathematical proofs by establishing a correspondence between proofs and programs. Research in this field has led to the development of highly technical constructions generalizing the method of forcing in set theory. In particular, models of realizability are models of ZF, and forcing models are special cases of realizability models.

03E70 ; 03F50 ; 03F55

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Logic and Foundations

The combinatorics of successors of singular cardinals presents a number of interesting open problems. We discuss the interactions at successors of singular cardinals of two strong combinatorial properties, the stationary set reflection and the tree property. Assuming the consistency of infinitely many supercompact cardinals, we force a model in which both the stationary set reflection and the tree property hold at $\aleph_{\omega^2+1}$. Moreover, we prove that the two principles are independent at this cardinal, indeed assuming the consistency of infinitely many supercompact cardinals it is possible to force a model in which the stationary set reflection holds, but the tree property fails at $\aleph_{\omega^2+1}$. This is a joint work with Menachem Magidor.
Keywords : forcing - large cardinals - successors of singular cardinals - stationary reflection - tree property
The combinatorics of successors of singular cardinals presents a number of interesting open problems. We discuss the interactions at successors of singular cardinals of two strong combinatorial properties, the stationary set reflection and the tree property. Assuming the consistency of infinitely many supercompact cardinals, we force a model in which both the stationary set reflection and the tree property hold at $\aleph_{\omega^2+1}$. ...

03E05 ; 03E35 ; 03E55

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