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Archive for Mathematical Logic

, Volume 55, Issue 5–6, pp 835–845 | Cite as

Fresh subsets of ultrapowers

  • Assaf Shani
Article

Abstract

Shelah and Stanley (Proc Am Math Soc 104(3):887–897, 1988) constructed a \(\kappa ^+\)-Aronszjan tree with an ascent path using \(\square _{\kappa }\). We show that \(\square _{\kappa ,2}\) does not imply the existence of Aronszajn trees with ascent paths. The proof goes through an intermediate combinatorial principle, which we investigate further.

Keywords

Aronszajn trees Square principles Forcing Fresh subsets 

Mathematics Subject Classification

03E05 03E35 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA

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