11 problems

Let $T$ be a countable complete theory and let $P$ be a distinguished unary predicate in its vocabulary. Assume that $T$ fails the Gaifman property; that is, assume that there exis…

The language and proof system of non-hypothetical logic are considered over the axioms of Peano Arithmetic, denoted by $\mathsf{PA}$, in a purely relational language. One may also…

Let $\Sigma_1$ and $\Sigma_2$ be disjoint signatures, and let ${\mathcal{T}}_1$ and ${\mathcal{T}}_2$ be decidable theories over them. Let ${\mathcal{T}}_1\oplus{\mathcal{T}}_2$ be…

Let ${{\mathsf{SPR}}}\xspace^+$ denote the behavioural formulation of the special principle of relativity, and let ${{\mathsf{SPR}_{{{\mathit{B}}}\xspace}}}\xspace$ denote the body…

Let $\mathbf A$ be a modeling, and for every first-order formula $\phi$ let $\langle\phi,\mathbf A\rangle$ denote its satisfaction probability in $\mathbf A$. Modeling-theory conje…

In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Logical systems are decidable if membership in their set o…

Let $L$ be a first-order language with countably many symbols, and let $T$ be a complete $L$-theory having infinite models. For a cardinal $\alpha$, let $I(T,\alpha)$ denote the nu…

Let $L_{\text{or}}=(+,-,\cdot,<,0,1)$ be the language of ordered rings, and let $L_{\exp}=L_{\text{or}}\cup\{\exp\}$, where $\exp$ is a unary function symbol. Let…

Fix an effective encoding of polynomials with integer coefficients in finitely many unknowns by finite strings over a finite alphabet (so that, for each $n\ge 1$, every…

Let $A$ be a finite alphabet. The set of generalized regular expressions over $A$ is defined inductively: $\emptyset$ and $a$ for each $a \in A$ are generalized regular expressions…

In model theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite Morley rank (see below).