Set Theory Is Interpretable in the Automorphism Group of an Infinitely Generated Free Group
نویسنده
چکیده
In [6] S. Shelah showed that in the endomorphism semi-group of an infinitely generated algebra which is free in a variety one can interpret some set theory. It follows from his results that, for an algebra Fκ which is free of infinite rank κ in a variety of algebras in a language L, if κ" rLr, then the first-order theory of the endomorphism semi-group of Fκ, Th(End(Fκ)), syntactically interprets Th(κ,L # ), the second-order theory of the cardinal κ. This means that for any second-order sentence χ of empty language there exists χ*, a first-order sentence of semi-group language, such that for any infinite cardinal κ" rLr,
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تاریخ انتشار 1997