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