Related papers: Supplement to the paper "On existence of log minim…
We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…
We discuss the relationship among various conjectures in the minimal model theory including the finite generation conjecture of the log canonical rings and the abundance conjecture. In particular, we show that the finite generation…
We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…
We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysohn's lemma for class $\mathcal{C}^q$ (see Section 3).
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
In this paper, we give a simple proof for the small cancellation conditions of the upper presentations of 2-bridge link groups, which holds the key to the proof of the main result of [1]. We also give an alternative proof of the main result…
In recent years, G\"odel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic…
Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic…
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
We prove several results relating the nonvanishing and the existence of good minimal models of different pairs that have the same underlying variety.
A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…
We prove that one can run the log minimal model program for log canonical $3$-fold pairs in characteristic $p>5$. In particular we prove the Cone Theorem, Contraction Theorem, the existence of flips and the existence of log minimal models…
In this paper we first prove a version of $L^{2}$ existence theorem for line bundles equipped a singular Hermitian metrics. Aa an application, we establish a vanishing theorem which generalizes the classical Nadel vanishing theorem.
In the realm of light logics deriving from linear logic, a number of variants of exponential rules have been investigated. The profusion of such proof systems induces the need for cut-elimination theorems for each logic, the proof of which…
This is the continuation of the article by the author that proves a broader class of families admitting the theorem of restriction of sections other than Abelian varieties and gives new examples of pseudo-N\'eron models. In this work, we…
We give down-to-earth proofs of the structure theorems for persistence modules.
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
In this paper, we prove a fine condensation theorem. This is quite similar to condensation theorems for pure extender mice in the literature, except that condensation for iteration strategies has been added to the mix.