The Stone-Weierstrass Theorem for compact Hausdorff spaces is a basic result of functional analysis with far-reaching consequences. We introduce an equational logic ? ? associated infinitary variety and show that the consequence Beth definability property , stating every implicit definition can be made explicit. Further, we define propositional ? by means Hilbert-style calculus prove strong com...

In two papers [3] and [4] we noted that in common practice many algebraic constructions are defined only ‘up to isomorphism’ rather than explicitly. We mentioned some questions raised by this fact, and we gave some partial answers. The present paper provides much fuller answers, though some questions remain open. Our main result, Theorem 4, says that there is a transitive model of Zermelo-Fraen...

The concept of definability of physical fields in a set-theoretical foundation is introduced. A set theory is selected in which we get mathematics enough to produce a nonlinear sigma model. Quantization of the model requires only a null postulate and is then shown to be necessary and sufficient for definability in the theory. We obtain scale invariance and compactification of the spatial dimens...

It is shown that if A is an analytic class of separable Banach spaces with separable dual, then the set A∗ = {Y : ∃X ∈ A with Y ∼= X∗} is analytic. The corresponding result for pre-duals is false.

Recent advances in distributed models and semantic epistemologies are never at odds with RAID [114, 188, 62, 70, 179, 68, 95, 54, 152, 191, 62, 59, 168, 148, 99, 58, 129, 128, 106, 191]. Given the current status of embedded epistemologies, security experts daringly desire the construction of thin clients. In order to solve this obstacle, we concentrate our efforts on arguing that e-commerce and...

Thanks to two stronger versions of predicate circumscription (one of the best known non-monotonic reasoning methods), we give a definitive answer to two old open problems. The first one is the problem of expressing domain circumscription in terms of predicate circumscription. The second one is the problem of definability of the circumscribed predicates, asked by Doyle in 1985, and never answere...

Equality in first-order logic is represented in the language by means of a logical symbol and so it is interpreted uniformly; the semantics says that its interpretation in any structure is the identity relation. This is the absolute notion of identity however, and in fact the only one deserving this name. But there is a related relation: the relation of indiscernibility. Given a structure for a...

In this paper, we use the notions of relative interpretations and definable models from mathematical logic to compare different ontologies and also to evaluate the limitations of particular ontologies. In particular, we characterize the relationship between the theories within the first-order PSL Ontology and two other ontologies – a first-order theory of time and Reiter’s second-order axiomati...

We describe the expressive power of temporal branching time logics that use the modalities EX and EF. We give a forbidden pattern characterization of the tree languages definable in three logics: EX, EF and EX+EF. The properties in these characterizations can be verified in polynomial time when given a minimal deterministic bottom-up tree automaton. We consider the definability problem for logi...