Related papers: Canonical Truth
We investigate, in ZFC, the behavior of abstract elementary classes (AECs) categorical in many successive small cardinals. We prove for example that a universal $\mathbb{L}_{\omega_1, \omega}$ sentence categorical on an end segment of…
We show (in ZFC) that the cardinality of a compact homogeneous space of countable tightness is no more than the size of the continuum.
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I…
We give an example of a countable theory T such that for every cardinal lambda >= aleph_2 there is a fully indiscernible set A of power lambda such that the principal types are dense over A, yet there is no atomic model of T over A. In…
The process of canonical quantization is redefined so that the classical and quantum theories coexist when \hbar>0, just as they do in the real world. This analysis not only supports conventional procedures, it also reveals new quantization…
We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to…
Much of the theory of large cardinals beyond a measurable cardinal concerns the structure of elementary embeddings of the universe of sets into inner models. This paper seeks to answer the question of whether the inner model uniquely…
Cardinal characteristics of the continuum represent the boundaries in size between the countable and the continuum with respect to certain properties of sets. They are often defined as the minimum sizes of families of reals that meet some…
The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality…
A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set-forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class-forcing extension which…
This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…
This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what…
This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free…
An observable canonical form is formulated for the set of rational systems on a variety each of which is a single-input-single-output, affine in the input, and a minimal realization of its response map. The equivalence relation for the…
Set-theoretical, physical, and intuitive notions of continuum are compared. It is shown that the independence of the continuum hypothesis determines status and properties of the set of intermediate cardinality. The intermediate set is a…
We introduce exacting cardinals and a strengthening of these, ultraexacting cardinals. These are natural large cardinals defined equivalently as weak forms of rank-Berkeley cardinals, strong forms of J\'onsson cardinals, or in terms of…
Let P be the direct product of countably many copies of the additive group Z of integers. We study, from a set-theoretic point of view, those subgroups of P for which all homomorphisms to Z annihilate all but finitely many of the standard…
Cubical type theory is an extension of Martin-L\"of type theory recently proposed by Cohen, Coquand, M\"ortberg and the author which allows for direct manipulation of $n$-dimensional cubes and where Voevodsky's Univalence Axiom is provable.…
We discuss the notion of \emph{uniform canonical bases}, both in an abstract manner and specifically for the theory of atomless $L_p$ lattices. We also discuss the connection between the definability of the set of uniform canonical bases…
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…