منابع مشابه
Implicit Definability in Arithmetic
We consider implicit definability over the natural number system N,+,×,=. We present a new proof of two theorems of Leo Harrington. The first theorem says that there exist implicitly definable subsets of N which are not explicitly definable from each other. The second theorem says that there exists a subset of N which is not implicitly definable but belongs to a countable, explicitly definable ...
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Pop proved that a smooth curve C over an ample field K with C(K) 6= ∅ has |K| many rational points. We strengthen this result by showing that there are |K| many rational points that do not lie in a given proper subfield, even after applying a rational map. As a consequence we gain insight into the structure of existentially definable subsets of ample fields. In particular, we prove that a perfe...
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In the framework of propositional Lukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly defining each of the rational elements in the standard semantics are explored, and based on that, a faithful interpretation of theories in Rational Pavelka logic ...
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Lambda deenability is characterized in categorical models of simply typed lambda calculus with type variables. A category-theoretic framework known as glueing or sconing is used to extend the Jung-Tiuryn characterization of lambda deenability JuT93], rst to ccc models, and then to categorical models of the calculus with type variables. Logical relations are now a well-established tool for study...
متن کاملSubfields of division algebras
Let A be a finitely generated domain of GK dimension less than 3 over a field K and let Q(A) denote the quotient division algebra of A. Using the ideas of Smoktunowicz, we show that if D is a finitely generated division subalgebras of Q(A) of GK dimension at least 2, then Q(A) is finite dimensional as a left D-vector space. We use this to show that if A is a finitely generated domain of GK dime...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2003
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1091122499