Related papers: IKP and Friends
In this note we prove some results in flat and differential $K$-theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
It is well-known that simple type theory is complete with respect to non-standard set-valued models. Completeness for standard models only holds with respect to certain extended classes of models, e.g., the class of cartesian closed…
We show that induction over $\Delta(\mathbb R)$-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
We study the properties of the constructible universe, L, over intuitionistic theories. We give an extended set of fundamental operations which is sufficient to generate the universe over Intuitionistic Kripke-Platek set theory without…
Choice and independence of premise principles play an important role in characterizing Kreisel's modified realizability and G\"odel's Dialectica interpretation. In this paper we show that a great many intuitionistic set theories are closed…
We give some background on uniform pro-p groups and the model theory of profinite NIP groups.
The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.
Independence of premise principles play an important role in characterizing the modified realizability and the Dialectica interpretations. In this paper we show that a great many intuitionistic set theories are closed under the…
This paper presents several independence results concerning the topos-valid and the intuitionistic (generalized) predicative theories of locales. In particular, certain consequences of the consistency of a general form of Troelstra's…
We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the novelty of the notion and its potential applications.
The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.
Inquisitive modal logic InqML is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they…
In this paper, we introduce $\textit{partial}$ dependency modality $\mathcal{D}$ into epistemic logic so as to reason about $\textit{partial}$ dependency relationship in Kripke models. The resulted dependence epistemic logic possesses…
We introduce a notion of realizability with ordinal Turing machines based on recognizability rather than computability, i.e., the ability to uniquely identify an object. We show that the arising concept of $r$-realizabilty has the property…
We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets,…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
We introduce a basic intuitionistic conditional logic $\mathsf{IntCK}$ that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that…