We prove that the first-order theory of the Medvedev degrees, the first-order theory of the Muchnik degrees, and the third-order theory of true arithmetic are pairwise recursively isomorphic (obtained independently by Lewis, Nies, and Sorbi [7]). We then restrict our attention to the degrees of closed sets and prove that the following theories are pairwise recursively isomorphic: the first-orde...

Lascar in [4] introduced the group Autf(N/A) of strong automorphisms over A, a normal subgroup of the group Aut(N/A) of all automorphisms overA of a modelN containingA. The quotient Aut(N/A)/Autf(N/A) is independent of the choice of N (for a big saturated model N and a small subset A ⊆ N ) and it is now called the Lascar group over A. Lascar showed in [4] that in the case of a very large class ...

This paper presents an encoding of a non-temporal fragment of the TLA language, which includes untyped set theory, functions, arithmetic expressions, and Hilbert’s ε operator, into many-sorted firstorder logic, the input language of state-of-the-art smt solvers. This translation, based on encoding techniques such as boolification, injection of unsorted expressions into sorted languages, term re...

We propose a logic-based rendition of electronic institutions – these are means to specify open agent organisations. We employ a simple notation based on first-order logic and set theory to represent an expressive class of electronic institutions. We also provide a formal semantics to our constructs and present a distributed implementation of a platform to enact electronic institutions specifie...

Lambda logic is the union of first order logic and lambda calculus. The purpose of this note is to give a complete and precise definition of the syntax of lambda logic, and explain its relations to first order logic and to simple type theory. This is a revised and expanded version of [6].

There are properties of nite structures that are expressible with the use of Hilbert's-operator in a manner that does not depend on the actual interpretation for-terms, but not expressible in plain rst-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in rst-order logic over nite structures. The present result also impl...

By a classifying topos for a first-order theory T, we mean a topos E such that, for any topos F , models of T in F correspond exactly to open geometric morphisms F → E . We show that not every (infinitary) first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate ‘smallness condition’, and we show that every Grothendieck topos arises as the c...

The examination of model-theoretic concepts in the context of general finite-dimensional algebras is a natural problem in applied model theory. Many of the most carefully studied and best understood algebraic objects are finite-dimensional algebras. Furthermore, the finiteness inherent to finite-dimensional algebras suggests that their theories might be amenable to exploration with techniques f...

A notion called Herbrand saturation is shown to provide the modeltheoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.