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The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction...
One-sided classifiers are computable devices which read the characteristic function of a set and output a sequence of guesses which converges to 1 iff the set on the input belongs to the gven class. Such a classifier istwo-sided if the sequence of its output in addition converges to 0 on setsnot...
We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable...
We show the relative consistency of ℵ1 satisfying a combinatorial property considered by David Fremlin (in the question DU from his list) in certain choiceless inner models. This is demonstrated by first proving the property is true for Ramsey cardinals. In contrast, we show that in ZFC, no...
We show that if G is a group of finite Morley rank, then the verbal subgroup is of finite width, where w is a concise word. As a byproduct, we show that if G is any abelian-by-finite group, then G
= is definable.
We show that, for each finite group G, there exists an axiomatization of the class of abelian-by-G groups with a single sentence. In the proof, we use the definability of the subgroups M
in an abelian-by-finite group M, and the Auslander-Reiten sequences for modules over an Artin algebra.
F. Oger proved that if A is a finite group, then the class of groups which are abelian-by-A can be axiomatized by a single first order sentence. It is established here that, in Oger's result, the word abelian cannot be replaced by group.
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