caa a22 4500 388039825 CHVBK 20180307125018.0 cr unu---uuuuu 161130e199809 xx s 000 0 eng 10.2307/2586726 doi S0022481200014730 pii (NATIONALLICENCE)cambridge-10.2307/2586726 Koszmider Piotr Department of Mathematics, Auburn University, Auburn, AL 36849, USA Departamento de Matemática, Universidade de São Paulo, Caixa Postal: 66281, São Paulo, S.P. CEP: 05315-970, Brasil E-mail: piotr@ime.usp.br On the existence of strong chains in ℘(ω1)/Fin [Elektronische Daten] [Piotr Koszmider] (X α: α < ω2) ⊂ ℘(ω1) is a strong chain in ℘(ω1)/Fin if and only if X β - X α is finite and X α - X β is uncountable for each β < α < ω1. We show that it is consistent that a strong chain in ℘(ω1) exists. On the other hand we show that it is consistent that there is a strongly almost-disjoint family in ℘(ω1) but no strong chain exists: is used to construct a c.c.c forcing that adds a strong chain and Chang's Conjecture to prove that there is no strong chain. Copyright © Association for Symbolic Logic 1998 The Journal of Symbolic Logic Cambridge University Press 63/3(1998-09), 1055-1062 0022-4812 63:3<1055 1998 63 JSL https://doi.org/10.2307/2586726 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586726 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Koszmider Piotr Department of Mathematics, Auburn University, Auburn, AL 36849, USA Departamento de Matemática, Universidade de São Paulo, Caixa Postal: 66281, São Paulo, S.P. CEP: 05315-970, Brasil E-mail: piotr@ime.usp.br NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/3(1998-09), 1055-1062 0022-4812 63:3<1055 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge