Independently axiomatizable ℒω1,ω theories

Independently Axiomatizable Lω1,ω Theories

In partial answer to a question posed by Arnie Miller [5] and X. Caicedo [2] we obtain sufficient conditions for an Lω1,ω theory to have an independent axiomatization. As a consequence we obtain two corollaries: If Vaught’s conjecture holds, then every Lω1,ω theory in a countable language has an independent axiomatization; every intersection of a family of Borel sets can be formed as the inters...

Quasi 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...

Properties of Independently Axiomatizable Bimodal Logics

In mono-modal logic there is a fair number of high-powered results on completeness covering large classes of modal systems, witness for example Fine [74,85] and Sahlqvist [75]. Mono-modal logic is therefore a well-understood subject in contrast to poly-modal logic where even the most elementary questions concerning completeness, decidability etc. have been left unanswered. Given that so many ap...

A Recursion-theoretic View of Axiomatizable Theories

Verification Issues in Combining Independently Consistent Theories

This paper addresses verification issues in combining knowledge bases or theories from different sources. Tile knowledge may be acquired using direct knowledge acquisition or inductive learning methods. Keeping the consistency of knowledge becomes all important issue when integrating two or more knowledge bases. Several independently consistent knowledge bases may give an inconsistent system wh...