Related papers: Sealing from Iterability
We show if a metric measure space admits a differentiable structure then porous sets have measure zero and hence the measure is pointwise doubling. We then give a construction to show if we only require an approximate differentiable…
We prove the sufficient conditions for convergence of a certain iterative process of order 2 for solving nonlinear functional equations, which does not require inverting the derivative. We translate and detail our results for a system of…
We consider simple models of tunneling of an object with intrinsic degrees of freedom. This important problem was not extensively studied until now, in spite of numerous applications in various areas of physics and astrophysics. We show…
There has been a significant interest in extending various modal logics with intersection, the most prominent examples being epistemic and doxastic logics with distributed knowledge. Completeness proofs for such logics tend to be…
Based on the work of Shelah, Kellner, and T\u{a}nasie (Fund. Math., 166(1-2):109-136, 2000 and Comment. Math. Univ. Carolin., 60(1):61-95, 2019), and the recent developments in the third author's master's thesis, we develop a general theory…
The purpose of testing a system with respect to a requirement is to refute the hypothesis that the system satisfies the requirement. We build a theory of tests and refutation based on the elementary notions of satisfaction and refinement.…
We adapt the classical notion of learning from text to computable structure theory. Our main result is a model-theoretic characterization of the learnability from text for classes of structures. We show that a family of structures is…
Value independence is enormously beneficial for reasoning about software systems at scale. These benefits carry over into the world of formal verification. Reasoning about programs algebraically is a simple affair in a proof assistant,…
The effectful forcing technique allows one to show that the denotation of a closed System T term of type $(\iota \to \iota) \to \iota$ in the set-theoretical model is a continuous function $(\mathbb{N} \to \mathbb{N}) \to \mathbb{N}$. For…
We develop a toolbox for forcing over arbitrary models of set theory without the axiom of choice. In particular, we introduce a variant of the countable chain condition and prove an iteration theorem that applies to many classical forcings…
We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using our method we prove that the forcing axiom for the class of all the small finitely proper posets is compatible with a…
In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…
Although good encryption functions are probabilistic, most symbolic models do not capture this aspect explicitly. A typical solution, recently used to prove the soundness of such models with respect to computational ones, is to explicitly…
Categories of models of algebraic theories have good categorical properties except for gluing. Building upon insights and examples from Synthetic Differential Geometry, we introduce a generalisation of models of algebraic theories to…
To efficiently simulate very thin, inextensible materials like cloth or paper, it is tempting to replace force-based thin-plate dynamics with hard isometry constraints. Unfortunately, naive formulations of the constraints induce membrane…
In this letter, we describe a very general procedure to obtain a causal fit of the permittivity of materials from experimental data with very few parameters. Unlike other closed forms proposed in the literature, the particularity of this…
In this paper we isolate the notion of Stratified class forcing and show that Stratification implies cofinality-preservation and is preserved by iterations with the appropriate support. Many familiar class forcings are stratified and…
In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple…
A buckled sheet offers a reservoir of material that can be unfurled at a later time. For sufficiently thin yet stiff materials, this geometric process has a striking mechanical feature: when the slack runs out, the material locks to further…
The connection between normalization by evaluation, logical predicates and semantic gluing constructions is a matter of folklore, worked out in varying degrees within the literature. In this note, we present an elementary version of the…