Shooting a club with finite conditions

Jindřich Zapletal

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Shooting a club with finite conditions

Jindřich Zapletal

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Abstract

We study cohabitation of the poset $P_S$ shooting a club through a given stationary subset $S$ of $\omega _1$ with finite conditions with other forcings. Sample results: (1) $P_S$ "sometimes" preserves presaturatedness of $NS_{\omega _1}$ (2) $P_S=P_T$ if $S=T mod NS_{\omega _1}$ (in Boolean algebra sense) (3) Cons ( one can embed $Q,$ the poset adding $\aleph _1$ Cohen reals, to $P_S$ such that reals in $V^Q$ are the same as reals in $V^{P_S}.$ )

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Jindřich Zapletal. 1994-03-10. Shooting a club with finite conditions. https://arxiv.org/abs/math/9403202

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