TY - JOUR
T1 - On a cardinal invariant related to the Haar measure problem
AU - Paolini, Gianluca
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - In [6], given a metrizable profinite group G, a cardinal invariant of the continuum fm(G) was introduced, and a positive solution to the Haar Measure Problem for G was given under the assumption that non(N) ≤ fm(G). We prove here that it is consistent with ZFC that there is a metrizable profinite group G* such that non(N) > fm(G*), thus demonstrating that the strategy of [6] does not suffice for a general solution to the Haar Measure Problem.
AB - In [6], given a metrizable profinite group G, a cardinal invariant of the continuum fm(G) was introduced, and a positive solution to the Haar Measure Problem for G was given under the assumption that non(N) ≤ fm(G). We prove here that it is consistent with ZFC that there is a metrizable profinite group G* such that non(N) > fm(G*), thus demonstrating that the strategy of [6] does not suffice for a general solution to the Haar Measure Problem.
UR - http://www.scopus.com/inward/record.url?scp=85079496813&partnerID=8YFLogxK
U2 - 10.1007/s11856-020-1975-2
DO - 10.1007/s11856-020-1975-2
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AN - SCOPUS:85079496813
SN - 0021-2172
VL - 236
SP - 305
EP - 316
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -