Forcing and construction schemes

DOI10.1007/S10474-019-00964-ZzbMATH Open1449.03018arXiv1711.11148OpenAlexW2962814246WikidataQ127630160 ScholiaQ127630160MaRDI QIDQ2330055

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Publication date: 18 October 2019

Published in: (Search for Journal in Brave)

Abstract: We investigate forcing and independence questions relating to construction schemes. We show that adding $kappageqomeg{a}_1$ 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${}_{omeg{a}_1}($K${}_m)$ and $n$-capturing are independent if $nleqm$ and incompatible if $n>m$.

Full work available at URL: https://arxiv.org/abs/1711.11148

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