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Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 27–41 | Cite as

Forcing and construction schemes

  • D. KalajdzievskiEmail author
  • F. Lopez
Article
  • 19 Downloads

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 \({\rm MA}_{\omega1}({\rm K}_{m}) \) and n-capturing are independent if \(n \leq m\) and incompatible if \(n>m\).

Key words and phrases

construction scheme Knaster hierarchy Cohen real 

Mathematics Subject Classification

03E05 03E35 03E65 

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Notes

Acknowledgement

The authors thank Osvaldo Guzmán for pointing out a nontrivial error on a previous version of Definition 3.1.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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