Related papers: $\Pi^0_4$ conservation of the Ordered Variable Wor…

We provide elementary algorithms for two preservation theorems for first-order sentences (FO) on the class \^ad of all finite structures of degree at most d: For each FO-sentence that is preserved under extensions (homomorphisms) on \^ad, a…

We investigate the expressive power of quantifier alternation hierarchy of first-order logic over words. This hierarchy includes the classes ${\Sigma}_i$ (sentences having at most $i$ blocks of quantifiers starting with an $\exists$) and…

Coherent causal memory (CCM) is causal memory in which prefixes of an execution can be mapped to global memory states in a consistent way. While CCM requires conflicting pairs of writes to be globally ordered, it allows writes to remain…

Ramsey's theorem states that each coloring has an infinite homogeneous set, but these sets can be arbitrarily spread out. Paul Erdos and Fred Galvin proved that for each coloring f, there is an infinite set that is "packed together" which…

The famous theorem by Chomsky and Sch\"utzenberger (CST) says that every context-free language $L$ over an alphabet $\Sigma$ is representable as $h(D \cap R)$, where $D$ is a Dyck language over a set $\Omega$ of brackets, $R$ is a local…

Let $\epsilon_{1},\ldots,\epsilon_{n}$ be a sequence of independent Rademacher random variables. We prove that there is a constant $c>0$ such that for any unit vectors $v_1,\ldots,v_n\in \mathbb{R}^2$, $$\Pr\left[||\epsilon_1…

In this note we conjecture Rogers-Ramanujan type colored partition identities for an array with odd number of rows w such that the first and the last row consist of even positive integers. In a strange way this is different from the…

We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]),…

Languages of the world vary concerning the order of subject, object and verb. The most frequent dominant orders are SOV and SVO, and researchers have tailored models to this fact. However, there are still languages whose dominant order does…

A well-ordering principle is a principle of the form: If $X$ is well-ordered then $F(X)$ is well-ordered, where $F$ is some natural operator transforming linear orders into linear orders. Many important subsystems of Second-order Arithmetic…

Let $w$ be a finite word over the alphabet $\{0,1\}$. For any natural number $n$, let $s_w(n)$ denote the number of occurrence of $w$ in the binary expansion of $n$ as a scattered subsequence. We study the behavior of the partial sum…

Given a fixed constraint language $\Gamma$, the conservative CSP over $\Gamma$ (denoted by c-CSP($\Gamma$)) is a variant of CSP($\Gamma$) where the domain of each variable can be restricted arbitrarily. A dichotomy is known for conservative…

In arXiv:2208.12944 it is shown that an ordinal $\sup_{N<\omega}\psi_{\Omega_{1}}(\varepsilon_{\Omega_{\mathbb{S}+N}+1})$ is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\ell^{r}+(M\prec_{\Sigma_{1}}V)$. In this…

We prove a general Ramsey theorem for trees with a successor operation. This theorem is a common generalization of the Carlson-Simpson Theorem and the Milliken Tree Theorem for regularly branching trees. Our theorem has a number of…

The Lov\'asz Local Lemma is a classic result in probability theory that is often used to prove the existence of combinatorial objects via the probabilistic method. In its simplest form, it states that if we have $n$ `bad events', each of…

In this paper, we introduce a hierarchy dividing the set $\{\sigma \in \Pi^1_2 : \Pi^1_1$-$\mathsf{CA}_0 \vdash \sigma\}$. Then, we give some characterizations of this set using weaker variants of some principles equivalent to…

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…

In this paper we consider $\phi^4$ theory in $4-\epsilon$ dimensions at the Wilson-Fisher fixed point where the theory becomes conformal. We extend the method in arXiv:1505.00963 for calculating the leading order term in the anomalous…

For any positive integer $n$, let $\mathcal{O}_{n}$ be the semigroup of all order-preserving full transformations on $X_{n}=\{1<\cdots <n\}$. For any $1\leq k\leq n$, let $\pi_{k}\in \mathcal{O}_{n}$ be the constant map defined by…

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…