Related papers: Stack semantics and the comparison of material and…
We give a model of dependent type theory with one univalent universe and propositional truncation interpreting a type as a stack, generalising the groupoid model of type theory. As an application, we show that countable choice cannot be…
It is well known that ZFC, despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the…
Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this paper we strive to give one class theory that allows for a…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…
This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisition. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are…
The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved…
We show that the Segal topos of derived stacks over simplicial commutative $k$-algebras, which can be used to model natural phenomena, has a subobject classifier, something we regard as being a source from which dynamics is generated. This…
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise…
Classic Topic Models are built under the Bag Of Words assumption, in which word position is ignored for simplicity. Besides, symmetric priors are typically used in most applications. In order to easily learn topics with different properties…
We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs. For this purpose, we…
We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…
The terms 'semantics' and 'ontology' are increasingly appearing together with 'explanation', not only in the scientific literature, but also in organizational communication. However, all of these terms are also being significantly…
We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (resp. connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
We define a variant of team semantics called multiteam semantics based on multisets and study the properties of various logics in this framework. In particular, we define natural probabilistic versions of inclusion and independence atoms…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
We construct higher categories of iterated spans, possibly equipped with extra structure in the form of "local systems", and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum…
We develop an axiomatic set theory -- the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to…
We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal…