A Co-free Construction for Elementary Doctrines

A Co-free Construction for Elementary Doctrines

We provide a construction which co-freely adds elementary structure to a primary doctrine in the sense of Lawvere. We show that the construction preserves all the first order logical structures that the starting doctrine may have. Moreover it forces the Principle of Propositional Extensionality when applied to tripos.

An Elementary Construction for a Non-elementary Procedure

We consider the problem of the product nite model property for binary products of modal logics. First we give a new proof for the product nite model property of the logic of products of Kripke frames, a result due to Shehtman. Then we modify the proof to obtain the same result for logics of products of Kripke frames satisfying any combination of seriality, re exivity and symmetry. We do not con...

Co-elementary Equivalence, Co-elementary Maps, and Generalized Arcs

By a generalized arc we mean a continuum with exactly two non-separating points; an arc is a metrizable generalized arc. It is well known that any two arcs are homeomorphic (to the real closed unit interval); we show that any two generalized arcs are co-elementarily equivalent, and that co-elementary images of generalized arcs are generalized arcs. We also show that if f : X → Y is a function b...

Construction of Thermodynamic Models for Elementary Teaching

A Universal Construction for (Co)Relations

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic interpretation for diagrams is given in terms of relations or corelations (generalised equivalence relations) of some kind. In this paper we show how semantic...