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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…

Differential Geometry · Mathematics 2014-07-17 Man-Ho Ho

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.…

Logic in Computer Science · Computer Science 2014-06-03 Arno Pauly , Matthew de Brecht

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.

Logic · Mathematics 2010-01-19 Dov Null Gabbay , Karl Schlechta

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…

Logic in Computer Science · Computer Science 2023-03-31 Steve Awodey , Florian Rabe

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…

Logic · Mathematics 2021-07-07 Anton Freund

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…

Artificial Intelligence · Computer Science 2013-04-16 Marc Maier , David Jensen

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…

Logic · Mathematics 2023-09-27 Richard Matthews , Michael Rathjen

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…

Logic · Mathematics 2024-12-02 Emanuele Frittaion , Takako Nemoto , Michael Rathjen

We give some background on uniform pro-p groups and the model theory of profinite NIP groups.

Group Theory · Mathematics 2017-05-23 Tim Clausen , Katrin Tent

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.

Formal Languages and Automata Theory · Computer Science 2015-09-02 Eric Rowland , Jeffrey Shallit

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…

Logic · Mathematics 2019-11-20 Takako Nemoto , Michael Rathjen

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…

Logic · Mathematics 2010-06-10 Giovanni Curi

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.

Logic · Mathematics 2014-11-04 Danko Ilik , Gyesik Lee , Hugo Herbelin

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.

Group Theory · Mathematics 2015-03-25 Rostislav Grigorchuk , Volodymyr Nekrashevych , Zoran Sunic

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…

Logic · Mathematics 2023-06-22 Ivano Ciardelli , Martin Otto

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…

Logic · Mathematics 2019-08-28 Xinyu Wang

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…

Logic · Mathematics 2024-08-14 Merlin Carl

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,…

Logic · Mathematics 2024-10-15 Amador Martin-Pizarro

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…

Artificial Intelligence · Computer Science 2014-01-07 Marc Maier , Katerina Marazopoulou , David Jensen

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…

Logic · Mathematics 2023-06-21 Grigory Olkhovikov