相关论文: On G\"odel's second incompleteness theorem
We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…
We propose an interpretation of the Newton's second law that is suggested by Galilean Relativity theory.
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
It is generally accepted that the incompleteness of first-order number theory (PA) is established by an application of Godel's proof. This paper shows that the arithmetization of the syntax of PA implies that the hypothesised class of PA…
Using nonstandard analysis, a very short and elementary proof of the Doob-Meyer decomposition and the Dol{\'e}ans Dade theorems is provided.
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
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 present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.
In an earlier paper, "Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem" (math/0206302), I argued that a constructive interpretation of Goedel's reasoning establishes any formal system of…
We describe a plan how to prove an effective Siegel theorem (about the exceptional Dirichlet character). We give a brief outline in Section 0. We give a more detailed plan in Sections 1-5. The missing details (mostly routine elementary…
In this work we proivied a new simpler proof of the global diffeomorphism theorem from [9] which we further apply to consider unique solvability of some abstract semilinear equations. Applications to the second order Dirichlet problem…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
In this short note we give counterexamples to several results related to extension theorems published recently.
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
Different from the view that information is objective reality, this paper adopts the idea that all information needs to be compiled by the interpreter before it can be observed. From the traditional complexity definition, this paper defines…