Finitely axiomatizable strongly minimal groups
نویسندگان
چکیده
منابع مشابه
Finitely axiomatizable strongly minimal groups
We show that if G is a strongly minimal finitely axiomatizable group, the division ring of quasi-endomorphisms of G must be an infinite finitely presented ring. Questions about finite axiomatizability of first order theories are nearly as old as model theory itself and seem at first glance to have a fairly syntactical flavor. But it was in order to show that totally categorical theories cannot ...
متن کاملComparing quasi-finitely axiomatizable and prime groups
An infinite f.g. group G is quasi-finitely axiomatizable (QFA) if there is a first-order sentence j such that G ! j, and if H is a f.g. group such that H ! j, then GGH. The first result is that all Baumslag–Solitar groups of the form ha; d j d"1ad 1⁄4 ai are QFA. A f.g. group G is a prime model if and only if there is a tuple g1; . . . ; gn generating G whose orbit (under the automorphisms of G...
متن کاملQuasi finitely axiomatizable totally categorical theories
As was shown in [2], totally categorical structures (i.e. which are categorical in all powers) are not finitely axiomatizable. On the other hand, the most simple totally categorical structures: infinite sets, infinite projective or affine geometries over a finite field, are quasi finitely axiomatizable (i.e. axiomatized by a finite number of axioms and the schema of infinity, we will use the ab...
متن کاملIteration Algebras are not Finitely Axiomatizable : Extended
Algebras whose underlying set is a complete partial order and whose termoperations are continuous may be equipped with a least fixed point operation μx.t. The set of all equations involving the μ-operation which hold in all continuous algebras determines the variety of iteration algebras. A simple argument is given here reducing the axiomatization of iteration algebras to that of Wilke algebras...
متن کاملML is not finitely axiomatizable over Cheq
We show that the Medvedev logic ML is not finitely axiomatizable over the logic Cheq of chequered subsets of R∞. This gives a negative solution to one of the questions raised by Litak [2].
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2012
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1264433908