TY - CHAP
T1 - Rich groups, weak second-order logic, and applications
AU - Kharlampovich, Olga
AU - Myasnikov, Alexei
AU - Sohrabi, Mahmood
N1 - Publisher Copyright:
© 2021 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2021/5/24
Y1 - 2021/5/24
N2 - In this chapter we initiate a study of first-order rich groups, i. e., groups where the first-order logic has the same power as the weak second-order logic. Surprisingly, there are quite a few finitely generated rich groups, they are somewhere inbetween hyperbolic and nilpotent groups (these are not rich). We provide some methods to prove that groups (and other structures) are rich and describe some of their properties. As corollaries we look at Malcev's problems in various groups.
AB - In this chapter we initiate a study of first-order rich groups, i. e., groups where the first-order logic has the same power as the weak second-order logic. Surprisingly, there are quite a few finitely generated rich groups, they are somewhere inbetween hyperbolic and nilpotent groups (these are not rich). We provide some methods to prove that groups (and other structures) are rich and describe some of their properties. As corollaries we look at Malcev's problems in various groups.
UR - http://www.scopus.com/inward/record.url?scp=85107319884&partnerID=8YFLogxK
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U2 - 10.1515/9783110719710-004
DO - 10.1515/9783110719710-004
M3 - Chapter
AN - SCOPUS:85107319884
SN - 9783110719666
SP - 127
EP - 191
BT - Groups and Model Theory
ER -