Shooting a club with finite conditions

arXivmath/9403202MaRDI QIDQ6503552

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

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