Related papers: Revisiting the conservativity of fixpoints over in…
In this paper we characterize the regularity structure, as well as show the global-in-time existence and uniqueness, of (energy) conservative solutions to the Hunter-Saxton equation by using the method of characteristics. The major…
We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretation is the intuitionistic counterpart of Ferreira and…
We introduce a modal logic FIL for Feferman interpretability. In this logic both the provability modality and the interpretability modality can come with a label. This label indicates that in the arithmetical interpretation the axiom set of…
Let H stand for the set of homeomorphisms on [0,1]. We prove the following dichotomy for Borel subsets A of [0,1]: either there exists a homeomorphism f in H such that the image f(A) contains no 3-term arithmetic progressions; or, for every…
We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of locally compact separable metric spaces. This complements work of Marde\v{s}i\'{c} and Prasolov…
We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison's conjecture on completely bounded homomorphisms holds for the…
We show that the Priess-Crampe & Ribenboim fixed point theorem is provable in $\mathsf{RCA}_0$. Furthermore, we show that Caristi's fixed point theorem for both Baire and Borel functions is equivalent to the transfinite leftmost path…
Floating-point arithmetic (FPA) is a mechanical representation of real arithmetic (RA), where each operation is replaced with a rounded counterpart. Various numerical properties can be verified by using SMT solvers that support the logic of…
This open problem, first posed by Erd{\omicron}s, was further explored by Terence Tao. Tao work shows that the series can converge conditionally, but only under a sufficiently strong form of the Hardy-Littlewood conjecture for k-primary…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
This part of a multi-paper project studies the lattice properties of the arithmetic mean ideals of B(H) introduced by Dykema, Figiel, Weiss, and Wodzicki. We prove: the lattices of all principal ideals, of arithmetic mean or arithmetic mean…
We propose a new axiomatisation of the alpha-equivalence relation for nominal terms, based on a primitive notion of fixed-point constraint. We show that the standard freshness relation between atoms and terms can be derived from the more…
The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T . We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$.…
We present a new set of reductions for derivations in natural deduction that can extract witnesses from closed derivations of simply existential formulas in Heyting Arithmetic (HA) plus the Excluded Middle Law restricted to simply…
The Majority is Stablest Theorem has numerous applications in hardness of approximation and social choice theory. We give a new proof of the Majority is Stablest Theorem by induction on the dimension of the discrete cube. Unlike the…
A natural deduction system for intuitionistic predicate logic with existential \ instantiation rule presented here uses Hilbert's $\e$-symbol. It is conservative over intuitionistic predicate logic. We provide a completeness proof for a…
We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal)…
In his constructive development of complex analysis, Errett Bishop used restrictive notions of homotopy and simple connectedness. Working in Bishop-style constructive mathematics, we prove Cauchy's integral theorem using the standard…
In the paper the well known Riemann Hypothesis is proven. The proof is based on uniform approximation of the zeta function discs of the critical strip placed to the right from the critical line.The basic moment is a use of a new mesure…
After reviewing the basic role of Lie's theory for the mathematics and physics of this century, we identify its limitations for the treatment of systems beyond the local-differential, Hamiltonian and canonical-unitary conditions of the…