Intuitionistic logic and implicit definability
نویسندگان
چکیده
منابع مشابه
Implicit definability of truth constants in Łukasiewicz logic
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 ...
متن کاملImplicit 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 ...
متن کاملLarisa Maksimova INTERPOLATION AND IMPLICIT DEFINABILITY IN EXTENSIONS OF THE PROVABILITY LOGIC ∗
The provability logic GL was in the field of interest of A.V. Kuznetsov, who had also formulated its intuitionistic analog—the intuitionistic provability logic—and investigated these two logics and their extensions. In the present paper, different versions of interpolation and of the Beth property in normal extensions of the provability logic GL are considered. It is proved that in a large clas...
متن کاملIntuitionistic Logic
There are basically two ways to view intuitionistic logic: (i) as a philosoph ical–foundational issue in mathematics, (ii) as a technical discipline within mathematical logic. Let us deal with the philosophical aspects first, they will provide the motivation for the subject. In doing so, we will follow L.E.J. Brouwer, the founding father of intuitionism. Brouwer did contribute little to intuiti...
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We study the expressive power of open formulas of dependence logic introduced in Väänänen [Dependence logic (Vol. 70 of London Mathematical Society Student Texts), 2007]. In particular, we answer a question raised by Wilfrid Hodges: how to characterize the sets of teams definable bymeans of identity only in dependence logic, or equivalently in independence friendly logic.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2000
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(99)00049-4