caa a22 4500 465811388 CHVBK 20180323112117.0 cr unu---uuuuu 170327e19900301xx s 000 0 eng 10.1007/BF02108862 doi (NATIONALLICENCE)springer-10.1007/BF02108862 Xishun Zhao Department of Mathematics, Henan Normal University, People's Republic of China aut The consistencies of MA, SOCA, OCA and ISA with KT (ω2) [Elektronische Daten] [Zhao Xishun] In this paper, we prove that ifZFC is consistent, then so are the following theories: $$\begin{gathered} ZFC + MA + KT(\omega _2 ) + 2^{\aleph _0 } = \aleph _2 , \hfill \\ ZFC + SOCA + KT(\omega _2 ), \hfill \\ ZFC + SOCA1 + KT(\omega _2 ), \hfill \\ ZFC + OCA + KT(\omega _2 ), \hfill \\ ZFC + ISA + KT(\omega _2 ), \hfill \\ \end{gathered} $$ whereMA denotes Martin's axiom.KT(ω 2) the statement:"There exists anω 2-Kurepa tree”, andSOCA, SOCA1,OCA andISA are axioms introduced in [1]. Springer-Verlag, 1990 Acta Mathematica Sinica Springer-Verlag 6/1(1990-03-01), 42-46 1439-8516 6:1<42 1990 6 10114 https://doi.org/10.1007/BF02108862 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02108862 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Xishun Zhao Department of Mathematics, Henan Normal University, People's Republic of China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica Springer-Verlag 6/1(1990-03-01), 42-46 1439-8516 6:1<42 1990 6 10114 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer