Related papers: A note on one-variable theorems for NSOP

We prove several theorems relating amenability of groups in various categories (discrete, definable, topological, automorphism group) to model-theoretic invariants (quotients by connected components, Lascar Galois group, G-compactness,…

We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…

We investigate the notions of strict independence and strict non-forking, and establish basic properties and connections between the two. In particular it follows from our investigation that in resilient theories strict non-forking is…

For sums $S_n=\sum_{k=1}^n X_k$, $n\ge 1$ of independent random variables $ X_k $ taking values in $\Z$ we prove, as a consequence of a more general result, that if (i) For some function $1\le \phi(t)\uparrow \infty $ as $t\to \infty$, and…

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures.…

A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement $\phi$ in some axiomatic system $T$, one looks for minimal subsystems of $T$ that allow deriving $\phi$. In…

We introduce the notions of triviality and order-triviality for global invariant types in an arbitrary first-order theory and show that they are well behaved in the NIP context. We show that these two notions agree for invariant global…

Unfortunately the proof of the main result of [1], Theorem 1, has a flaw. Namely, Lemma 13 used in the proof of Proposition 11 is correct only under an additional assumption that the operator $A$ is normal (adjoint for the one-sided shift…

Kikyo and Shelah showed that if $T$ is a theory with the Strict Order Property in some first-order language $\mathcal{L}$, then in the expanded language $\mathcal{L}_\sigma := \mathcal{L}\cup\{\sigma\}$ with a new unary function symbol…

The $O(N)$ non-linear sigma model (NLSM) is an example of field theory on a target space with nontrivial geometry. One interesting feature of NLSM is asymptotic freedom, which makes perturbative calculations interesting. Given the successes…

We establish conditions in the spirit of the T1 theorem of David and Journ\'e which guarantee the boundedness of \nabla T on L^p(\R^n), where T is an integral transformation and 1<p<\infty. These are natural size and regularity conditions…

Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…

We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly…

We show that $\ell_p$ norms are characterized as the unique norms which are both invariant under coordinate permutation and multiplicative with respect to tensor products. Similarly, the $L_p$ norms are the unique rearrangement-invariant…

Given a structure $\mathcal{M}$ and a stably embedded $\emptyset$-definable set $Q$, we prove tameness preservation results when enriching the induced structure on $Q$ by some further structure $\mathcal{Q}$. In particular, we show that if…

We answer a question of Pakhomov by showing that there is a consistent, c.e. theory $T$ such that no theory which is definitionally equivalent to $T$ has a computable model. A key tool in our proof is the model-theoretic notion of mutual…

For which unary predicates $P_1, \ldots, P_m$ is the MSO theory of the structure $\langle \mathbb{N}; <, P_1, \ldots, P_m \rangle$ decidable? We survey the state of the art, leading us to investigate combinatorial properties of…

We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes $q$ adaptive queries and…

In this paper we give an ordinal analysis of a set theory extending ${\sf KP}\ell^{r}$ with an axiom stating that `there exists a transitive set $M$ such that $M\prec_{\Sigma_{1}}V$'.

In this note we give a particularly short and simple proof of the following theorem of Karrass and Solitar. Let $H$ be a finitely generated subgroup of a free group $F$ with infinite index $[F:H]$. Then there is a nontrivial normal subgroup…