TY - JOUR
T1 - On uncountable hypersimple unidimensional theories
AU - Shami, Ziv
PY - 2014/2
Y1 - 2014/2
N2 - We extend the dichotomy between 1-basedness and supersimplicity proved in Shami (J Lond Math Soc 83(2):309-332, 2011). The generalization we get is to arbitrary language, with no restrictions on the topology [we do not demand type-definabilty of the open set in the definition of essential 1-basedness from Shami (J Lond Math Soc 83(2):309-332, 2011)]. We conclude that every (possibly uncountable) hypersimple unidimensional theory that is not s-essentially 1-based by means of the forking topology is supersimple. We also obtain a strong version of the above dichotomy in the case where the language is countable.
AB - We extend the dichotomy between 1-basedness and supersimplicity proved in Shami (J Lond Math Soc 83(2):309-332, 2011). The generalization we get is to arbitrary language, with no restrictions on the topology [we do not demand type-definabilty of the open set in the definition of essential 1-basedness from Shami (J Lond Math Soc 83(2):309-332, 2011)]. We conclude that every (possibly uncountable) hypersimple unidimensional theory that is not s-essentially 1-based by means of the forking topology is supersimple. We also obtain a strong version of the above dichotomy in the case where the language is countable.
KW - 1-based
KW - Forking-topology
KW - Simple theory
KW - Unidimensional theory
UR - http://www.scopus.com/inward/record.url?scp=84892521310&partnerID=8YFLogxK
U2 - 10.1007/s00153-013-0362-7
DO - 10.1007/s00153-013-0362-7
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84892521310
SN - 0933-5846
VL - 53
SP - 203
EP - 210
JO - Archive for Mathematical Logic
JF - Archive for Mathematical Logic
IS - 1-2
ER -