$\aleph_0$-categoricity over a predicate.

Computable Categoricity versus Relative Computable Categoricity

We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1-decidable computably categorical structure is relatively ∆2-categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also...

Constraint-Based Invariant Inference over Predicate Abstraction

This paper describes a constraint-based invariant generation technique for proving the validity of safety assertions over the domain of predicate abstraction in an interprocedural setting. The key idea of the technique is to represent each invariant in bounded DNF form by means of boolean indicator variables, one for each predicate p and each disjunct d denoting whether p is present in d or not...

Categoricity of computable infinitary theories

Categoricity and Scott Families

Effective model theory is an area of logic that analyzes the effective content of the typical notions and results of model theory and universal algebra. Typical notions in model theory and universal algebra are languages and structures, theories and models, models and their submodels, automorphisms and isomorphisms, embeddings and elementary embeddings. In this paper languages, structures, and ...

Categoricity and Infinitary Logics

We point out a gap in Shelah’s proof of the following result: Claim 0.1. Let K be an abstract elementary class categorical in unboundedly many cardinals. Then there exists a cardinal λ such that whenever M,N ∈ K have size at least λ, M ≤ N if and only if M L∞,LS(K)+ N . The importance of the claim lies in the following theorem, implicit in Shelah’s work: Theorem 0.2. Assume the claim. Let K be ...