Related papers: Norms on possibilities I: forcing with trees and c…
Imposing constraints on the output of a Deep Neural Net is one way to improve the quality of its predictions while loosening the requirements for labeled training data. Such constraints are usually imposed as soft constraints by adding new…
We isolate a combinatorial property of capacities leading to a construction of proper forcings. Then we show that many classical capacities such as the Newtonian capacity satisfy the property.
We introduce a method of constructing a forcing along a simplified $(\kappa,1)$-morass such that the forcing satisfies the $\kappa$-chain condition. Alternatively, this may be seen as a method to thin out a larger forcing to get a chain…
We introduce several properties of forcing notions which imply that their lambda-support iterations are lambda-proper. Our methods and techniques refine those studied in math.LO/9906024, math.LO/0210205, math.LO/0508272 and math.LO/0605067,…
We study relationships between various set theoretic compactness principles, focusing on the interplay between the three families of combinatorial objects or principles mentioned in the title. Specifically, we show the following. (1) Strong…
We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…
I argue that John Norton's notions of empirical, hypothetical, and counterfactual possibility can be successfully used to analyze counterintuitive examples of physical possibility and align better with modal intuitions of practicing…
We give a brief survey on the interplay between forcing axioms and various other non-constructive principles widely used in many fields of abstract mathematics, such as the axiom of choice and Baire's category theorem. First of all we…
Let $\mathcal{SN}$ be the $\sigma$-ideal of the strong measure zero sets of reals. We present general properties of forcing notions that allow to control of the additivity of $\mathcal{SN}$ after finite support iterations. This is applied…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach uses the language of functors and natural…
The present paper has three themes. First, we continue the investigations started in Judah, Roslanowski and Shelah \math.LO/9310224 and Roslanowski and Shelah math.LO/9807172, math.LO/9703222, and we investigate the method of norms on…
We introduce more properties of forcing notions which imply that their lambda-support iterations are lambda-proper, where lambda is an inaccessible cardinal. This paper is a direct continuation of section A.2 of math.LO/0210205. As an…
We study how to infer new choices from previous choices in a conservative manner. To make such inferences, we use the theory of choice functions: a unifying mathematical framework for conservative decision making that allows one to impose…
The Maximality Principle MP is a scheme which states that if a sentence of the language of ZFC is true in some forcing extension V^P, and remains true in any further forcing extension of V^P, then it is true in all forcing extensions of V.…
I prove forcing preservation theorems for products of definable partial orders preserving the cofinality of the meager or null ideal. Rectangular Ramsey theorems for related ideals follow from the proofs.
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
Evaluating conjunctive queries and solving constraint satisfaction problems are fundamental problems in database theory and artificial intelligence, respectively. These problems are NP-hard, so that several research efforts have been made…
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…
Current approaches to neural network verification focus on specifications that target small regions around known input data points, such as local robustness. Thus, using these approaches, we can not obtain guarantees for inputs that are not…