English
Related papers

Related papers: Generalized Silver and Miller measurability

200 papers

We show a general relationship between a superposition of macroscopically distinct states and sensitivity in quantum metrology. Generalized cat states are defined by using an index which extracts the coherence between macroscopically…

Quantum Physics · Physics 2019-09-18 Mamiko Tatsuta , Yuichiro Matsuzaki , Akira Shimizu

We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly kappa+ many normal measures on the least measurable cardinal kappa. This answers a question of Stewart Baldwin. The methods…

Logic · Mathematics 2007-05-23 Arthur W. Apter , James Cummings , Joel David Hamkins

We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra…

Rings and Algebras · Mathematics 2019-02-20 Alex Bartel , Hendrik W. Lenstra

Measurable sets are defined as those locally approximable, in a certain sense, by sets in the given algebra (or ring). A corresponding measure extension theorem is proved. It is also shown that a set is locally approximable in the mentioned…

Classical Analysis and ODEs · Mathematics 2017-02-14 Iosif Pinelis

We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…

Logic · Mathematics 2013-12-25 Saharon Shelah

Generalized Yang-Mills theories are constructed, that can use fields other than vector as gauge fields. Their geometric interpretation is studied. An application to the Glashow-Weinberg-Salam model is briefly review, and some related…

High Energy Physics - Theory · Physics 2007-05-23 M. Chaves

In this paper we study the Borel reducibility of Borel equivalence relations, including some orbit equivalence relations, on the generalised Baire space $\kappa^\kappa$ for an uncountable $\kappa$ with the property…

Logic · Mathematics 2014-08-20 Sy-David Friedman , Tapani Hyttinen , Vadim Kulikov

We define a notion of coordinatization for $\aleph_0$-categorical structures which is, like Lie coordinatized structures in [2], a certain kind of expansion of a tree. We show that a structure which is coordinatized, in a certain strong…

Logic · Mathematics 2023-03-17 Mostafa Mirabi

We study several intertwined hierarchies between $\kappa$-Ramsey cardinals and measurable cardinals to illuminate the structure of the large cardinal hierarchy in this region. In particular, we study baby versions of measurability…

Logic · Mathematics 2023-11-22 Victoria Gitman , Philipp Schlicht

In the context of large cardinals, the classical diamond principle Diamond_kappa is easily strengthened in natural ways. When kappa is a measurable cardinal, for example, one might ask that a Diamond_kappa sequence anticipate every subset…

Logic · Mathematics 2007-05-23 Joel David Hamkins

A general formalism is developed that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for…

High Energy Physics - Theory · Physics 2009-11-10 Marija Dimitrijevic , Larisa Jonke , Lutz Moeller , Efrossini Tsouchnika , Julius Wess , Michael Wohlgenannt

The general structure of the matter Kahler metric in the $\kappa^{2/3}$ expansion of Horava-Witten M-theory with nonstandard embeddings is examined. It is shown that phenomenological models based on this structure can lead to Yukawa and…

High Energy Physics - Theory · Physics 2015-06-25 R. Arnowitt , B. Dutta

This paper investigates the problem of extending measure theory to non-separable structures, from generalized descriptive set theory to a broader class of spaces beyond this framework. While various notions, such as the ideal of measure…

Logic · Mathematics 2026-01-21 Claudio Agostini , Fernando Barrera , Vincenzo Dimonte

In this paper we study the theories of the infinite-branching tree and the $r$-regular tree, and show that both of them are pseudofinite. Moreover, we show that they can be realized by infinite ultraproducts of polynomial exact classes of…

Logic · Mathematics 2026-01-14 Darío García , Melissa Robles

Given an uncountable cardinal $\kappa$, we consider the question of whether subsets of the power set of $\kappa$ that are usually constructed with the help of the Axiom of Choice are definable by $\Sigma_1$-formulas that only use the…

Logic · Mathematics 2023-09-20 Philipp Lücke , Sandra Müller

Non-forking is one of the most important notions in modern model theory capturing the idea of a generic extension of a type (which is a far-reaching generalization of the concept of a generic point of a variety). To a countable first-order…

Logic · Mathematics 2015-08-14 Artem Chernikov , Itay Kaplan , Saharon Shelah

We generalize the basic theory of universally Baire sets of $2^\omega$ to a theory of universally Baire subsets of $2^\kappa$. We show that the fundamental characterizations of the property of being universally Baire have natural…

Logic · Mathematics 2024-12-24 Daisuke Ikegami , Matteo Viale

The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Bahram Mashhoon

Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…

Physics and Society · Physics 2007-06-20 V. I. Danilov , A. Lambert-Mogiliansky

We introduce a new topological generalization of the $\sigma$-projective hierarchy, not limited to Polish spaces. Earlier attempts have replaced $^{\omega}\omega$ by $^{\kappa}\kappa$, for $\kappa$ regular uncountable, or replaced countable…

Logic · Mathematics 2022-10-13 Iván Ongay-Valverde , Franklin D. Tall