Related papers: Completeness in local positive logic

We present the notions of positively complete theory and general forms of amalgamation in the framework of positive logic. We explore the fundamental properties of positively complete theories and study the behaviour of companion theories…

Positive logic is a generalisation of full first-order logic that does not have negation built in. Still, many model-theoretic ideas, tools and techniques work perfectly fine in positive logic. Importantly, there is a compactness theorem.…

The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…

We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for…

We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…

With the aim of developing the concepts of positive logic and in response to a question that was asked by Poizat in one of his articles, I wrote this article. The main topic is the study of compactness in the extension as a compact…

We study type spaces and saturation for local positive logic.

We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.

Lindstr\"om's Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward L\"owenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious…

One of the nice properties of the first-order logic is the compactness of satisfiability. It state that a finitely satisfiable theory is satisfiable. However, different degrees of satisfiability in many-valued logics, poses various kind of…

In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver…

The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are…

We study positively closed and strongly positively closed topos-valued models of coherent theories. Positively closed is a global notion (it is defined in terms of all possible outgoing homomorphisms), while strongly positively closed is a…

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…

We characterise non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations…

We study the amalgamation property in positive logic. We give some connections between the amalgamation property and Robinson theories, model-complete theories and the Hausdorff property.

In this paper, we study several propositional team logics that are closed under unions, including propositional inclusion logic. We prove that all these logics are expressively complete, and we introduce sound and complete systems of…

We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general…

We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topological models of a countable theory

We begin the study of categorical logic for continuous model theory. In particular, we 1. introduce the notions of metric logical categories and functors as categorical equivalents of a metric theory and interpretations, 2. prove a…