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arXiv · 1711.11148

Forcing and Construction Schemes

Damjan Kalajdzievski·Fulgencio Lopez
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Abstract

We investigate forcing and independence questions relating to construction schemes. We show that adding $\kappa\geq\omega_1$ Cohen reals adds a capturing construction scheme. We study the weaker structure of $n$-capturing construction schemes and show that it is consistent to have $n$-capturing construction schemes but no $(n+1)$-capturing construction schemes. We also study the relation of $n$-capturing with the $m$-Knaster hierarchy and show that MA$_{\omega_1}($K$_m)$ and $n$-capturing are independent if $n\leq m$ and incompatible if $n>m$.

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Damjan Kalajdzievski, Fulgencio Lopez. 2017-11-29. Forcing and Construction Schemes. https://arxiv.org/abs/1711.11148

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