Geodesic
Sigma-Prikry forcing I: The Axioms
Canadian journal of mathematics, Tome 73 (2021) no. 5, pp. 1205-1238

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DOI

We introduce a class of notions of forcing which we call $\Sigma $-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality are $\Sigma $-Prikry. We show that given a $\Sigma $-Prikry poset $\mathbb P$ and a name for a non-reflecting stationary set T, there exists a corresponding $\Sigma $-Prikry poset that projects to $\mathbb P$ and kills the stationarity of T. Then, in a sequel to this paper, we develop an iteration scheme for $\Sigma $-Prikry posets. Putting the two works together, we obtain a proof of the following.Theorem. If $\kappa $ is the limit of a countable increasing sequence of supercompact cardinals, then there exists a forcing extension in which $\kappa $ remains a strong limit cardinal, every finite collection of stationary subsets of $\kappa ^+$ reflects simultaneously, and $2^\kappa =\kappa ^{++}$.
DOI : 10.4153/S0008414X20000425
Mots-clés : Sigma-Prikry forcing, stationary reflection, singular cardinals hypothesis 
Poveda, Alejandro; Rinot, Assaf; Sinapova, Dima. Sigma-Prikry forcing I: The Axioms. Canadian journal of mathematics, Tome 73 (2021) no. 5, pp. 1205-1238. doi: 10.4153/S0008414X20000425
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     title = {Sigma-Prikry forcing {I:} {The} {Axioms}},
     journal = {Canadian journal of mathematics},
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     year = {2021},
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