Israel Journal of Mathematics

, Volume 118, Issue 1, pp 289–315

On strong chains of uncountable functions


DOI: 10.1007/BF02803525

Cite this article as:
Koszmider, P. Isr. J. Math. (2000) 118: 289. doi:10.1007/BF02803525


For functionsf,g1 → ω1, where ω1 is the first uncountable cardinal, we write thatf≪g if and only if {ξ ∈ ω1 :f(ξ)≥g(ξ)} is finite. We prove the consistency of the existence of a well-ordered increasing ≪-chain of length ω12, solving a problem of A. Hajnal. The methods previously developed by us involveforcing with side conditions in morasses which is a variation on Todorcevic'sforcing with models as side conditions. The paper is self-contained and requires from the reader knowledge of Kunen's textbook and some basic experience with proper forcing and elementary submodels.

Copyright information

© Hebrew University 2000

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de São PauloSão PauloBrasil

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