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BOOLEAN ALGEBRAS IN AST
Author(s) -
Schumacher Klaus
Publication year - 1992
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.19920380135
Subject(s) - stone's representation theorem for boolean algebras , complete boolean algebra , free boolean algebra , boolean algebras canonically defined , two element boolean algebra , countable set , boolean algebra , mathematics , set (abstract data type) , interior algebra , parity function , boolean expression , discrete mathematics , algebra over a field , pure mathematics , boolean function , computer science , algebra representation , jordan algebra , programming language
In this paper we investigate Boolean algebras and their subalgebras in Alternative Set Theory (AST). We show that any two countable atomless Boolean algebras are isomorphic and we give an example of such a Boolean algebra. One other main result is, that there is an infinite Boolean algebra freely generated by a set. At the end of the paper we show that the sentence “There is no non‐trivial free group which is a set” is consistent with AST.