We examine the reverse-mathematical strength of several theorems in classical and effective model theory concerning first-order theories and their number of models. We prove that, among these, most are equivalent to one of the familiar systems RCA0, WKL0, or ACA0. We are led to a purely model-theoretic statement that implies WKL0 but refutes ACA0 over RCA0.

A probability distribution can be given to the set of isomorphism classes of models with universe {1, . . . , n} of a sentence in rst-order logic. We study the entropy of this distribution and derive a result from the 0-1 law for rst-order sentences.

We introduce the notion of the burden of a partial type in a complete first-order theory and call a theory strong if all types have almost finite burden. In a simple theory it is the supremum of the weights of all extensions of the type, and a simple theory is strong if and only if all types have finite weight. A theory without the independence property is strong if and only if it is strongly d...

We consider all positive fragments of Tarski’s representable relation algebras and determine whether the equational and quasiequational theories of these fragments are finitely axiomatizable in first-order logic. We also look at extending the signature with reflexive, transitive closure and the residuals of composition.

Simple type theory, also known as higher-order logic, is a natural extension of first-order logic which is simple, elegant, highly expressive, and practical. This paper surveys the virtues of simple type theory and attempts to show that simple type theory is an attractive alternative to first-order logic for practical-minded scientists, engineers, and mathematicians. It recommends that simple t...

We build an example that generalizes [HS90] to uncountable cases. In particular, our example yields a sentence ψ ∈ L(2λ)+,ω that is categorical in λ, λ, . . . , λ but not in ik+1(λ) . This is connected with the Loś Conjecture and with Shelah’s own conjecture and construction of excellent classes for the ψ ∈ Lω1,ω case. 1 The Loś Conjecture, without excellence Early results on the Categoricity S...

We introduce the notion of a preindependence relation between subsets of the big model of a complete first-order theory, an abstraction of the properties which numerous concrete notions such as forking, dividing, thorn-forking, thorn-dividing, splitting or finite satisfiability share in all complete theories. We examine the relation between four additional axioms (extension, local character, fu...

We examine the relationship between Dependence Logic and game logics. A variant of Dynamic Game Logic, called Transition Logic, is developed, and we show that its relationship with Dependence Logic is comparable to the one between First-Order Logic and Dynamic Game Logic discussed by van Benthem. This suggests a new perspective on the interpretation of Dependence Logic formulas, in terms of ass...

Inquisitive first-order logic, InqBQ, extends classical first-order logic with questions. From a technical perspective, InqBQ allows us to talk about a plurality of first-order structures, expressing not only facts about each structure in isolation, but also about how these structures relate to each other. We describe an Ehrenfeucht-Fräıssé game for InqBQ and show that this characterizes the ex...

Recent research in diagnosis (Mcllraith, 1997; Thielscher, 1997; McIlraith, 1998) extends earlier works in diagnosis fi’om first principles by using an action theory instead of a first-order theory to describe the correct behavior of the system in consideration. The action theory allows us to reason about actions and their effects. Thus, when an action does not yield the expected effects someth...