naa a22 4500 510783562 CHVBK 20180411083255.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11856-013-0007-x doi (NATIONALLICENCE)springer-10.1007/s11856-013-0007-x Subcompact cardinals, squares, and stationary reflection [Elektronische Daten] [Andrew Brooke-Taylor, Sy-David Friedman] We generalise Jensen's result on the incompatibility of subcompactness with □. We show that α +-subcompactness of some cardinal less than or equal to α precludes $${\square _\alpha }$$ , but also that square may be forced to hold everywhere where this obstruction is not present. The forcing also preserves other strong large cardinals. Similar results are also given for stationary reflection, with a corresponding strengthening of the large cardinal assumption involved. Finally, we refine the analysis by considering Schimmerling's hierarchy of weak squares, showing which cases are precluded by α +-subcompactness, and again we demonstrate the optimality of our results by forcing the strongest possible squares under these restrictions to hold. Hebrew University Magnes Press, 2013 Brooke-Taylor Andrew Graduate School of System Informatics, Kobe University, Rokko-dai 1-1, 657-8501, Nada, Kobe, Japan aut Friedman Sy-David Kurt Gödel Research Center for Mathematical Logic, Währinger Strasse 25, A1020, Vienna, Austria aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 197/1(2013-10-01), 453-473 0021-2172 197:1<453 2013 197 11856 https://doi.org/10.1007/s11856-013-0007-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0007-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brooke-Taylor Andrew Graduate School of System Informatics, Kobe University, Rokko-dai 1-1, 657-8501, Nada, Kobe, Japan aut NATIONALLICENCE 700 1- Friedman Sy-David Kurt Gödel Research Center for Mathematical Logic, Währinger Strasse 25, A1020, Vienna, Austria aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 197/1(2013-10-01), 453-473 0021-2172 197:1<453 2013 197 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer