Related papers: Some results on $\mathbb{R}$-computable structures
We axiomatize and generalize Markov's approach to the continuity problem for Type 1 computable functions, i.e. the problem of finding sufficient conditions on a computable topological space to obtain a theorem of the form "computable…
We propose a definition of computable manifold by introducing computability as a structure that we impose to a given topological manifold, just in the same way as differentiability or piecewise linearity are defined for smooth and PL…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear…
Using an iterative tree construction we show that for simple computable subsets of the Cantor space Hausdorff, constructive and computable dimensions might be incomputable.
Computer simulations that demonstrate the valueof novel approaches are crucial to developing more flexibleand robust power systems operations with high penetrations ofrenewable energy at multiple geographic and temporal scales.However,…
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is actually computable. Miller proved that finite-dimensional spheres have computable type, Iljazovi\'c and other authors established the property…
This short paper proposes to learn models of satisfiability modulo theories (SMT) formulas during solving. Specifically, we focus on infinite models for problems in the logic of linear arithmetic with uninterpreted functions (UFLIA). The…
We consider the following problem for various infinite time machines. If a real is computable relative to large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
This paper extends the class of ordinal regression models with a structured interpretation of the problem by applying a novel treatment of encoded labels. The net effect of this is to transform the underlying problem from an ordinal…
This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems. Exciting recent developments include new methods involving…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
A modified realisability interpretation of infinitary logic is formalised and proved sound in constructive type theory (CTT). The logic considered subsumes first order logic. The interpretation makes it possible to extract programs with…
Causal inference, a critical tool for informing business decisions, traditionally relies heavily on structured data. However, in many real-world scenarios, such data can be incomplete or unavailable. This paper presents a framework that…
Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize…
We study uncountable structures similar to the Fra\"iss\'e limits. The standard inductive arguments from the Fra\"iss\'e theory are replaced by forcing, so the structures we obtain are highly sensitive to the universe of set theory. In…
We examine the relation of BSS-reducibility on subsets of the real numbers. The question was asked recently (and anonymously) whether it is possible for the halting problem H in BSS-computation to be BSS-reducible to a countable set.…
Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The precise relationship of the various definitions used in the two…