Related papers: Sweet & Sour and other flavours of ccc forcing not…

Let V be the universe of sets and V_{\alpha} the sets of rank \leq\alpha. We develop some axiom schemata for set theory based on the following three assumptions: 1. V \models ZFC 2. V is large with respect to the class of ordinals 3. V is…

What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…

Four algorithms giving rise to graceful graphs from a known (non)graceful graph are described. Some necessary conditions for a graph to be highly graceful and critical are given. Finally some conjectures are made on graceful, critical and…

In \cite{MV} we defined and proved the consistency of the principle ${\rm GM}^+(\omega_3,\omega_1)$ which implies that many consequences of strong forcing axioms hold simultaneously at $\omega_2$ and $\omega_3$. In this paper we formulate a…

We study an extensive connection between factor forcings of Borel subsets of Polish spaces modulo a sigma-ideal, and factor forcings of subsets of countable sets modulo an ideal.

We present the classical theory of preservation of $\sqsubset$-unbounded families in generic extensions by ccc posets, where $\sqsubset$ is a definable relation of certain type on spaces of real numbers, typically associated with some…

Under what condition is a random constraint satisfaction problem hard to refute by the sum-of-squares (SoS) algorithm? A sufficient condition is t-wise uniformity, that is, each constraint has a t-wise uniform distribution of satisfying…

Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…

People are commonly interested in predicting a statistical property of a random event such as mean and variance. Proper scoring rules assess the quality of predictions and require that the expected score gets uniquely maximized at the…

In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing.…

In Mathias forcing, conditions are pairs $(D,S)$ of sets of natural numbers, in which $D$ is finite, $S$ is infinite, and $\max D < \min S$. The Turing degrees and computational characteristics of generics for this forcing in the special…

In this work, we study the socially fair $k$-median/$k$-means problem. We are given a set of points $P$ in a metric space $\mathcal{X}$ with a distance function $d(.,.)$. There are $\ell$ groups: $P_1,\dotsc,P_{\ell} \subseteq P$. We are…

Using forcing with measured creatures we build a universe of set theory in which: (a) every sup-measurable function f:RxR-->R is measurable, and (b) every function f:R-->R is continuous on a non-measurable set. This answers a question of…

Motivated by the intimate connection between the strong CP problem and the flavor structure of the Standard Model, we present a flavor model that revives and extends the classic ${m_u=0}$ solution to the strong CP problem. QCD is embedded…

Recent studies have significantly improved the state-of-the-art on common-sense reasoning (CSR) benchmarks like the Winograd Schema Challenge (WSC) and SWAG. The question we ask in this paper is whether improved performance on these…

We present preservation theorems for countable support iteration of nep forcing notions satisfying ``old reals are not Lebesgue null'' and ``old reals are not meager''. (Nep is a generalization of Suslin proper.) We also give some results…

We present a systematic empirical study of prompt engineering for formal mathematical reasoning in the context of the SAIR Equational Theories Stage 1 competition. The task requires deciding whether one equational law implies another over…

We investigate the strength of a randomness notion $\mathcal R$ as a set-existence principle in second-order arithmetic: for each $Z$ there is an $X$ that is $\mathcal R$-random relative to $Z$. We show that the equivalence between…

Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations 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.…