Related papers: Iterating Semi-proper Forcing using Virtual Models
We present a method for iterating semiproper forcing which uses side conditions and is inspired by the technique recently introduced by Neeman.
We prove various iteration theorems for forcing classes related to subproper and subcomplete forcing, introduced by Jensen. In the first part, we use revised countable support iterations, and show that 1) the class of subproper,…
These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…
This is an expository paper about several sophisticated forcing techniques closely related to standard finite support iterations of ccc partial orders. We focus on the four topics of ultrapowers of forcing notions, iterations along…
We introduce a simplified framework for ord-transitive models and Shelah's non elementary proper (nep) theory. We also introduce a new construction for the countable support nep iteration.
We deal with an iteration theorem of forcing notion with a kind of countable support of nice enough forcing notion which is proper aleph_2-c.c. forcing notions. We then look at some special cases (Q_D 's preceded by random forcing).
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
The preservation theorems for semi-properness, hemi-properness, and pseudo-completeness hold for countable support iterations as well as revised countable support iterations, notwithstanding the fact that the "factor lemma" fails for the…
We look for a parallel to the notion of ``proper forcing'' among lambda-complete forcing notions not collapsing lambda^+ . We suggest such a definition and prove that it is preserved by suitable iterations.
We investigate the effectiveness of reinforcement learning methods for finetuning large language models when transitioning from offline to semi-online to fully online regimes for both verifiable and non-verifiable tasks. Our experiments…
Neural machine translation models usually adopt the teacher forcing strategy for training which requires the predicted sequence matches ground truth word by word and forces the probability of each prediction to approach a 0-1 distribution.…
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.…
This work considers the application of the virtual element method to plane hyperelasticity problems with a novel approach to the selection of stabilization parameters. The method is applied to a range of numerical examples and well known…
The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II [3] the method is…
We lay the ground for an Isabelle/ZF formalization of Cohen's technique of forcing. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize the definition of forcing notions as…
Fix a set-theoretic universe $V$. We look at small extensions of $V$ as generalised degrees of computability over $V$. We also formalise and investigate the complexity of certain methods one can use to define, in $V$, subclasses of degrees…
I survey an array of topics in set theory in the context of a novel class of forcing notions: subcomplete forcing. Subcompleteness was originally defined by Ronald Jensen. I have attempted to make the subject somewhat more approachable to…
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…
A Temporal Neural Network (TNN) architecture for implementing efficient online reinforcement learning is proposed and studied via simulation. The proposed T-learning system is composed of a frontend TNN that implements online unsupervised…
The desire to use reinforcement learning in safety-critical settings has inspired a recent interest in formal methods for learning algorithms. Existing formal methods for learning and optimization primarily consider the problem of…