Related papers: Forcing with random variables in bounded arithmeti…
In the present paper we are interested in properties of forcing notions which measure in a sense the distance between the ground model reals and the reals in the extension. We look at the ways the ``new'' reals can be aproximated by ``old''…
We make use of a forcing technique for extending Boolean algebras. The same type of forcing was employed in [BK81], [Kos99], and elsewhere. Using and modifying a lemma of Koszmider, and using CH, we obtain an atomless BA, A such that f(A) =…
The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver's theorem and Bukovsk\'y's theorem assert that set-generic extensions of a given…
Posner and Robinson (1981) proved that if $S \subseteq \omega$ is non-computable, then there exists a $G \subseteq \omega$ such that $S \oplus G \geq_T G'$. Shore and Slaman (1999) extended this result to all $n \in \omega$, by showing that…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
This paper introduces Force Matching (ForM), a novel framework for generative modeling that represents an initial exploration into leveraging special relativistic mechanics to enhance the stability of the sampling process. By incorporating…
It is well known that the completeness theorem for $\mathrm{L}_{\omega_1\omega}$ fails with respect to Tarski semantics. Mansfield showed that it holds for $\mathrm{L}_{\infty\infty}$ if one replaces Tarski semantics with boolean valued…
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…
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.
In this article we introduce and study hyperclass-forcing (where the conditions of the forcing notion are themselves classes) in the context of an extension of Morse-Kelley class theory, called MK$^{**}$. We define this forcing by using a…
The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories…
This is an overview about a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along $\omega_1$ is given. Then its direct limit satisfies ccc by…
It is shown that the boldface maximality principle for subcomplete forcing, together with the assumption that the universe has only set-many grounds, implies the existence of a (parameter-free) definable well-ordering of…
The aim of these lectures is to give a short introduction to forcing. We will avoid metamathematical issues as much as possible and similarly we will avoid performing the actual construction of forcing. We assume familiarity with basic…
Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic…
Measurability with respect to ideals is tightly connected with absoluteness principles for certain forcing notions. We study a uniformization principle that postulates the existence of a uniformizing function on a large set, relative to a…
It was realized early on that topologies can model constructive systems, as the open sets form a Heyting algebra. After the development of forcing, in the form of Boolean-valued models, it became clear that, just as over ZF any…
Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions. In the present work, we consider the well-known Burgers equation with random…
Statisticians have recently developed propensity score methods to improve generalizations from randomized experiments that do not employ random sampling. However, these methods typically rely on assumptions whose plausibility may be…
We study the interplay between properties of measures on a Boolean algebra A and forcing names for ultrafilters on A. We show that several well known measure theoretic properties of Boolean algebras (such as supporting a strictly positive…