Forcing and Construction Schemes

2017/11/29 by Kalajdzievski, Damjan, Lopez, Fulgencio · 2 citations
#03E05 #03E35 #03E65 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1711.11148

Abstract

We investigate forcing and independence questions relating to construction schemes. We show that adding κ≥ω₁ 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_ω1(K_m) and n-capturing are independent if n≤ m and incompatible if n>m.

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• Forcing Axioms and construction schemes
• There may be an n-entangled set but no n+1-entangled sets

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