Archive for Mathematical Logic

, Volume 55, Issue 5–6, pp 835–845

Fresh subsets of ultrapowers


DOI: 10.1007/s00153-016-0497-4

Cite this article as:
Shani, A. Arch. Math. Logic (2016) 55: 835. doi:10.1007/s00153-016-0497-4


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.


Aronszajn trees Square principles Forcing Fresh subsets 

Mathematics Subject Classification

03E05 03E35 

Funding information

Funder NameGrant NumberFunding Note
Directorate for Mathematical and Physical Sciences (US)
  • 1044604

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA

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