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- W4313303570 abstract "We introduce a new and natural stationary set preserving forcing $mathbb P^{c-c}({lambda},{mu})$ that (under ${rm NS}$ precipitous + existence of $H_{theta}^#$ for a sufficiently large regular ${theta}$) increases the second uniform indiscernible $u_2$ beyond some given ordinal ${lambda}$. The forcing $mathbb P^{c-c}$ shares this property with forcings defined in [9] and [2]. As a main tool we use certain natural open two player games which are of independent interest, viz. the capturing games $G^{cap}(X)$ and the catching-capturing games $G^{c-c}(X)$. In particular, these games are used to isolate a special family of countable elementary submodels $M prec H_{theta}$ that occur as side conditions in $mathbb P^{c-c}$ and thus allow to control the forcing in a strong way." @default.
- W4313303570 created "2023-01-06" @default.
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- W4313303570 date "2022-12-28" @default.
- W4313303570 modified "2023-10-02" @default.
- W4313303570 title "Increasing the second uniform indiscernible by strongly ssp forcing" @default.
- W4313303570 doi "https://doi.org/10.48550/arxiv.2212.13797" @default.
- W4313303570 hasPublicationYear "2022" @default.
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