Related papers: A Note on McGee's {\omega}-Inconsistency Result
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of…
In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.
We improve constants in the Rademacher-Menchov inequality.
We prove that total instability is a generic phenomenon in the real analytic class of electromagnetic Lagrangian systems under a weak magnetism hypothesis. The main object in the proof is an adaptation of the McGehee blowup for these…
This proof of Godel's first incompleteness theorem doesn't require omega-consistency, nor does it refer to codes of negated sentences as in Rosser's. It begins from where Godel's usual proof ends, and stalks it till it ends proving it.
Given sets $\Phi_1=\{\phi_{11},...,\phi_{1u(1)}\}, ...,\Phi_{z}=\{\phi_{z1},...,\phi_{zu(z)}\}$ of boolean formulas, a formula $\omega$ follows from the conjunction $\bigwedge\Phi_i= \bigwedge \phi_{ij}$ iff $\neg \omega\wedge…
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
We prove a new and unified GAGA theorem. This recovers all analytic and formal GAGA results in the literature, and is also valid in the non-noetherian setting. Our method can also be used to establish various Lefschetz theorems and…
In this note, we show various versions of holomorphic Morse inequalities tensoring with a coherent sheaf.
We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.
The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.
We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.
Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.
This paper presents two observability inequalities for the heat equation over $\Omega\times(0,T)$. In the first one, the observation is from a subset of positive measure in $\Omega\times(0,T)$, while in the second, the observation is from a…
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
This paper examines a denumerable version of the nested-set theorem and derives from it a contradiction involving the formal consistency of the actual infinity assumed by the Axiom of Infinity.
We prove some extensions of Andrews inequality.
We prove that the consistency strength of Martin's Maximum restricted to partial orders of cardinality $\omega_1$ follows from the consistency of ZFC.