Related papers: Varieties of class-theoretic potentialism
We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\Sigma$ formulas. We consider theories whose axioms are implications between…
Several definitions of classicality are considered, such as P-representability, generalized coherent states and separable states. These notions are treated under a simple and general definition based on convex sets, which enables the use of…
The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…
We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…
Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of…
We define an $\infty$-category of rational motives for inverse limits of algebraic stacks, so-called pro-algebraic stacks. We show that it admits a $6$-functor formalism for certain classes of morphisms. On pro-schemes, we show that this…
Existing generalization theories of supervised learning typically take a holistic approach and provide bounds for the expected generalization over the whole data distribution, which implicitly assumes that the model generalizes similarly…
Classification may not be reliable for several reasons: noise in the data, insufficient input information, overlapping distributions and sharp definition of classes. Faced with several possibilities neural network may in such cases still be…
We consider the problem of characterizing isomorphisms of types, or, equivalently, constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials. Mostly relying on results about…
Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…
We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
Berge's maximum theorem gives conditions ensuring the continuity of an optimised function as a parameter changes. In this paper we state and prove the maximum theorem in terms of the theory of monoidal topology and the theory of double…
Many results have been established that show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper is to show several results about solvability concerning the…
As performance gains through scaling data and/or model size experience diminishing returns, it is becoming increasingly popular to turn to ensembling, where the predictions of multiple models are combined to improve accuracy. In this paper,…
Historically, appearance of the quantum theory led to a prevailing view that Nature is indeterministic. The arguments for the indeterminism and proposals for indeterministic and deterministic approaches are reviewed. These include collapse…
We use a novel type of epistemic logic, employing comparative knowledge assertions, to analyze the relative epistemic powers of individuals or groups of agents. Such comparative assertions can express that a group has the potential to…
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.