Denjoy-Carleman classes of differentiable functions, say in Roumieu's form: Given a log-convex sequence $M_n$ of positive number denote by $C_M=C_M(\mathbb{R}^n,0)$ the ring o …

Suppose $D$ is a non-empty set and $\{ R_i : i \in \mathbb{N} \}$ is a family of binary relations on sequences over $D$ so that $R_i \subseteq D^i \times D^i$. Let $R_\omega \subse …

What are some of the common popular stable theories that are known to be dp-minimal (or not dp-minimal)? Some dp-minimal examples I am aware of are strongly minimal theories, supe …

Are there known (preferably ``concrete'') examples of a ring $R$ (commutative, with 1) such that: $\bullet$ the first order theory of $R$ is undecidable, but $\bullet$ the posit …

If $M$ and $N$ are two $L$-structures, and $f: M \rightarrow N$ is an elementary extension, then given any subset $A$ of $M$, $f$ induces in a natural way a morphism $S^M_n(A) \rig …

In a previous post I asked about the definability of a function that can be "approximated" by a uniformly definable family of functions. Nevertheless, the notion of approximation I …

Let $T$ be a first order theory, $M$ a model of $T$ equipped with a topology with a definable basis (i.e. every basic open is definable with parameters). Let $F: M\rightarrow M$ be …

I am trying to find some examples of Fraïssé classes that do not have the strong amalgamation property. Anyone?

Peano Arithmetic (PA) models have a prime number structure and commutativity of addition and multiplication. Presperger arithmetic (PrA) models of arithmetic have addition without …

Let the first-order language ${\mathcal{L}}$ have a single binary predicate $P$. Consider the structure whose underlying set is ${\mathbb{Z}}$, the integers, and an ordered pair $( …

In "Admissible Sets and Structures" page 101 theorem 5.8 Barwise introduces a weird form of his compactness theorem in which there are two theories $T$ and $T'$ both $\Sigma_1$, su …

Given language $L$. $P$ is a 1-place predicate in $L$. Let language $L_0 = L \setminus {P}$. Let $\sigma$ be a sentence of $L$ (may contain symbol $P$). $\mathfrak{A}$ is a structu …

excuse me for bad writing style. 1) When a complete theory has quantifier elimination? 2) When a theory that has quantifier elimination property is complete? give examples of com …

Hi all! Is there anything like Gödel's constructible universe for New Foundations? More precisely, I would like a process for taking a model $M$ of NF, and using it to build a mod …

Consider the first order theory of fields, whose language contains constant symbol $0$ for additive identity, constant symbol $1$ for multiplicative identity, function symbol $A(x, …