Related papers: Existence in NSOP$_1$ theories

Mekler constructed a way to produce a pure group from any given structure where the construction preserves $\kappa$-stability for any cardinal $\kappa$. Not only the stability, it is known that his construction preserves various…

We prove a non-linear version of a theorem of Grayson which is an analogue of the Fundamental Theorem of Algebraic $K$-theory and identify the $K$-theory of the endomorphism category over a space $X$ in terms of reduced $K$-theory of a…

We initiate a systematic study of \emph{generic stability independence} and introduce the class of \emph{treeless theories} in which this notion of independence is particularly well-behaved. We show that the class of treeless theories…

We prove that graded K-theory is universal among oriented Borel-Moore homology theories with a multiplicative periodic formal group law.

Existence theorem is proven for the generating equations of the split involution constraint algebra. The structure of the general solution is established, and the characteristic arbitrariness in generating functions is described.

We prove a general local existence theorem for nonlinear systems of Cauchy-Riemann operator of any order in one complex variable with initial values at a given point, which is a counterpart of local existence of ODE.

We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $\pi_0$. We prove this as a consequence of a more general devissage result for stable infinity…

Mark Kisin proved that a certain restriction functor on crystalline p-adic representations is fully faithful. In this paper, we prove the torsion analogue of Kisin's theorem.

I present a criterion for all-order finiteness in $N=1$ SYM theories. The structure of the supercurrent anomaly, the Callan-Symanzik equation and the supersymmetric non-renormalization theorem for chiral anomalies are the essential…

In a nutshell, we show that polynomials and nested polytopes are topological, algebraic and algorithmically equivalent. Given two polytops $A\subseteq B$ and a number $k$, the Nested Polytope Problem (NPP) asks, if there exists a polytope…

Let $N$ be a prime 3-manifold that is not a closed graph manifold. Building on a result of Hongbin Sun and using a result of Asaf Hadari we show that for every $k\in\Bbb{N}$ there exists a finite cover $\tilde{N}$ of $N$ such that…

We confirm a conjecture of Sun on the expansions of $n(m^k-1)/(m-1)$ in base $m$.

It is proven that in the universal splitexact equivariant algebraic $KK$-theory for algebras, the $K$-theory groups coincide with classical $K$-theory in the sense of Phillips. This partially answers a question raised by Kasparov.

We prove the existence of maximizers for a general family of restrictions operators, up to the end-point. We also provide some counterxamples in the end-point case.

We show that the ample degree of a stable theory with trivial forking is preserved when we consider the corresponding theory of belles paires, if it exists. This result also applies to the theory of $H$-structures of a trivial theory of…

Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.

We introduce and examine some special classes of invariant types$\unicode{x2014}$bi-invariant, strongly bi-invariant, extendibly invariant, and reliably invariant types$\unicode{x2014}$and show that they are related to certain…

By a theorem of Suslin, a Tor-unital (not necessarily unital) ring satisfies excision in algebraic K-theory. We give a new and direct proof of Suslin's result based on an exact sequence of categories of perfect modules. In fact, we prove a…

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…

In this work we prove the undecidability (and $\Sigma^0_1$-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective…