相关论文: Current Mathematics Appears to Be Inconsistent
We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.
By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…
We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].
In this paper, the abc conjecture is negated under certain conditions
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
We improve the backward compatibility of stableKanren to run miniKanren programs. stableKanren is a miniKanren extension capable of non-monotonic reasoning through stable model semantics. However, standard miniKanren programs that produce…
We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the…
The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet…
We formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of ${\rm I\Delta_0}$ whose Herbrand Consistency is not provable in the thoery ${\rm I\Delta_0}$. We…
Some inequalities for different types of convexity are established.
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often…
We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…
We investigate a result on convergence of double sequences of numbers and how it extends to measurable functions.
This paper recalls some classical motivations in fluid dynamics leading to a partial differential equation which is prescribed on a domain whose boundary possesses two connected components, one endowed with a Dirichlet datum, and the other…
A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Koml\'os conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry.