Premium
Elementary Properties of the Finite Ranks
Author(s) -
Dawar Anuj,
Doets Kees,
Lindell Steven,
Weinstein Scott
Publication year - 1998
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19980440306
Subject(s) - mathematics , class (philosophy) , hierarchy , order (exchange) , combinatorics , discrete mathematics , class hierarchy , computer science , artificial intelligence , programming language , object oriented programming , finance , economics , market economy
This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first‐order definable over the class of finite directed graphs and that this class admits a first‐order definable global linear order. We apply this last result to show that FO(<, BIT) = FO(BIT).