Related papers: Universal forcing notions and ideals
We give arguments for and prove the consistency of some internal forcing axioms.
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
It is known that the set of possible cofinalities $\mathrm{pcf}(A)$ has good properties if $A$ is a progressive interval of regular cardinals. In this paper, we give an interval of regular cardinals $A$ such that $\mathrm{pcf}(A)$ has no…
We show that the cofinalities of both the Miller ideal m^0 (the sigma-ideal naturally related to Miller forcing) and the Laver ideal ell^0 (related to Laver forcing) are larger than the size of the continuum in ZFC.
We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…
We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof is by interpolation and uses the Mapping Reflection Principle.
Universal definitions of irredundance for X-set parameters are presented using blocking sets. This approach is modeled on (domination) irredundance (which uses closed neighborhoods as blocking sets) and zero forcing irredundance (which uses…
In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…
Let $\mathcal{SN}$ be the strong measure zero $\sigma$-ideal. We prove a result providing bounds for $\mathrm{cof}(\mathcal{SN})$ which implies Yorioka's characterization of the cofinality of the strong measure zero. In addition, we use…
Let $D$ be an infinite discrete set of measurable cardinals. It is shown that generalized Prikry forcing to add a countable sequence to each cardinal in $D$ is subcomplete. To do this it is shown that a simplified version of generalized…
We propose a classification of group properties according to whether they can be deduced from the assumption that a group's subgroup lattice contains an interval isomorphic to some lattice. We are able to classify a few group properties as…
In computer science, combinatorics, and model theory, the VC dimension is a central notion underlying far-reaching topics such as error rate for decision rules, combinatorial measurements of classes of finite structures, and neo-stability…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
The notion of $\theta$-FAM-linkedness, introduced in the second author's master thesis, is a formalization of the notion of strong FAM limits for intervals, whose initial form and applications have appeared in the work of Saharon Shelah,…
We consider the modality "$\varphi$ is true in every $\sigma$-centered forcing extension", denoted $\square\varphi$, and its dual "$\varphi$ is true in some $\sigma$-centered forcing extension", denoted $\lozenge\varphi$ (where $\varphi$ is…
We consider the problem of identifying universal low-dimensional features from high-dimensional data for inference tasks in settings involving learning. For such problems, we introduce natural notions of universality and we show a local…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
It is shown that any finitely generated subring of a global field has a universal first-order definition in its fraction field. This covers Koenigsmann's result for the ring of integers and its subsequent extensions to rings of integers in…
We analyze several ``strong meager'' properties for filters on the natural numbers between the classical Baire property and a filter being $F_\sigma$. Two such properties have been studied by Talagrand and a few more combinatorial ones are…