Related papers: Supplement to the paper "On existence of log minim…
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.
In this paper, we prove the termination of 4-fold semi-stable log flips under the assumption that there always exist 4-fold (semi-stable) log flips.
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
We give a light introduction to some recent developments in Mori theory, and to our recent direct proof of the finite generation of the canonical ring.
We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…
We define a notion of model for the $\lambda$$\Pi$-calculus modulo theory and prove a soundness theorem. We then define a notion of super-consistency and prove that proof reduction terminates in the $\lambda$$\Pi$-calculus modulo any…
We present a tool that automates termination proofs for recursive definitions by mining existing termination theorems.
In this paper, we show that the minimal model theory does not hold in characteristic two. More precisely, we construct counter-examples to the relative abundance conjecture.
We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
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…
We give a simple proof of a crucial lemma that is established in [1, Lemma 2.1] by induction, and plays important roles in that paper and [2].
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
We prove that the finite generation of adjoint rings proved in [Cascini and Lazi\'c] implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Contraction theorems, the existence of flips, and termination…
In this short note we give counterexamples to several results related to extension theorems published recently.
This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.
An emended and improved version of the present paper has been archived in math-ph/0505057, and a preliminary account of its content has been published in Phys.Rev.Lett. 92, 60601, (2004). Moreover, in order to prove the relevance of…
This paper has been withdrawn due to a crucial error in the proof of the main theorem