Deduction in many-valued logics: a survey.
Deduction over graphs under constraints : a soundness and completeness theorem
Deductive systems of BCK-algebras
In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator of a deductive system is the the pseudocomplement of . These results are more general than that the similar results given by M. Kondo in [7].
Definability and forcing in E-recursion.
Definability degrees for classes in the alternative set theory
Definability in structures of finite valency
Definability in the extended arithmetic of ordinal numbers [Book]
Definability in the lattice of equational theories of semigroups.
Definability of arithmetical operations from binary quadratic forms
Definability of principal congruences in equivalential algebras
Definability of small puncture sets
We characterize the class of definable families of countable sets for which there is a single countable definable set intersecting every element of the family.
Definability within structures related to Pascal’s triangle modulo an integer
Let Sq denote the set of squares, and let be the squaring function restricted to powers of n; let ⊥ denote the coprimeness relation. Let . For every integer n ≥ 2 addition and multiplication are definable in the structures ⟨ℕ; Bn,⊥⟩ and ⟨ℕ; Bn,Sq⟩; thus their elementary theories are undecidable. On the other hand, for every prime p the elementary theory of ⟨ℕ; Bp,SQp⟩ is decidable.
Definable Davies' theorem
We prove the following descriptive set-theoretic analogue of a theorem of R. O. Davies: Every Σ¹₂ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ¹₂ functions if and only if all reals are constructible.
...-definable functionals and ... Conversion.
Definable functions in the -categorical weakly circularly minimal structures.
Definable hereditary families in the projective hierarchy
We show that if ℱ is a hereditary family of subsets of satisfying certain definable conditions, then the reals are precisely the reals α such that . This generalizes the results for measure and category. Appropriate generalization to the higher levels of the projective hierarchy is obtained under Projective Determinacy. Application of this result to the -encodable reals is also shown.
Definable orthogonality classes in accessible categories are small
We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopěnka’s principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Lévy hierarchy. For example, the statement that, for a class of morphisms in a locally presentable category of structures, the orthogonal class of objects is a small-orthogonality...
Definable quantifiers in second order arithmetic and elementary extensions of ω-models [Book]
Definable Ramsey and definable Erdös ordinals.
Definable sets over finite fields.