Related papers: Uniformization and Internal Absoluteness
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
We generalise results by Sacks and Tanaka concerning measure-theoretic uniformity for hyperarithmetical sets and a basis theorem for $\Pi^1_1$-sets of positive measure to computability and semicomputability relative to the Suslin…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…
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…
Let \alpha be a countable ordinal and \P(\alpha) the collection of its subsets isomorphic to \alpha. We show that the separative quotient of the set \P (\alpha) ordered by the inclusion is isomorphic to a forcing product of iterated reduced…
We investigate the $\sigma$-porosity of certain known ideals of subsets of natural numbers. Porosity is a notion of smallness in metric spaces that is stronger than nowhere density. Analogously, $\sigma$-porosity is a strengthening of…
A notion of sectional regularity for a homogeneous ideal $I$, which measures the regularity of its generic sections with respect to linear spaces of various dimensions, is introduced. It is related to axial constants defined as the…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
The half-open real unit interval (0,1] is closed under the ordinary multiplication and its residuum. The corresponding infinite-valued propositional logic has as its equivalent algebraic semantics the equational class of cancellative hoops.…
In this article, for generalized projective spaces with any weights, we prove four main theorems in three different contexts where the Unital Set Condition USC (Definition $2.8$) on ideals is further examined. In the first context we prove,…
Given an analytic equivalence relation, we tend to wonder whether it is Borel. When it is non Borel, there is always the hope it will be Borel on a "large" set -- nonmeager or of positive measure. That has led Kanovei, Sabok and Zapletal to…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
Effective versions of strong measure zero sets are developed for various levels of complexity and computability. It is shown that the sets can be equivalently defined using a generalization of supermartingales called odds supermartingales,…
We show that one can force the Measuring principle without adding any new reals. We also show that it is consistent with the large continuum. These results answer two famous questions of Justin Moore.
We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the second…
Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on…