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On strong chains of uncountable functions
 Piotr Koszmider
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For functionsf,g:ω_{1} → ω_{1}, where ω_{1} is the first uncountable cardinal, we write thatf≪g if and only if {ξ ∈ ω_{1} :f(ξ)≥g(ξ)} is finite. We prove the consistency of the existence of a wellordered increasing ≪chain of length ω_{12}, 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 selfcontained and requires from the reader knowledge of Kunen's textbook and some basic experience with proper forcing and elementary submodels.
Some of the research leading to this paper was supported by NSF of USA Grant DMS9505098 held by the author at Auburn University, AL, USA, some was done while the author was visiting Ohio University at Athens, OH, USA from September 1997 till March 1998, and some was done at Universidade de São Paulo, where the author has been working since 1998. We would like to thank the settheory groups from these universities for their hospitality.
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 Title
 On strong chains of uncountable functions
 Journal

Israel Journal of Mathematics
Volume 118, Issue 1 , pp 289315
 Cover Date
 20001201
 DOI
 10.1007/BF02803525
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
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 Authors

 Piotr Koszmider ^{(1)}
 Author Affiliations

 1. Departamento de Matemática, Universidade de São Paulo, Caixa Postal: 66281, CEP: 05315970, São Paulo, SP, Brasil