相关论文: Logic Blog 2016
The 2015 Logic Blog contains a large variety of results connected to logic, some of them unlikely to be submitted to a journal. For the first time there is a group theory part. There are results in higher randomness, and in computable…
The 2022 logic blog has concentrated on the connections of group theory and logic. It discusses Gardam's 2021 refutation of the Higman/ Kaplansky unit conjecture, and its connections to logic and to computation. The rest is about…
The blog has several entries on group theory interacting with computability and wider logic, several open questions, and an entry on undecidability in physics.
The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of $\Pi^1_1$ randomness and higher weak 2 randomness is determined. 2. Reverse mathematics and its relationship to randomness. For…
The blog focusses on algorithmic randomness and its connections to quantum information theory, group theory and its connections to logic, and computability analogs of cardinal characteristics.
The blog is somewhat shorter than in previous years, It contains new insights in a variety of areas, including computability, quantum algorithmic version of the SMB theorem, descriptions of groups (both discrete and profinite), metric…
The 2014 Logic Blog starts with open questions from the May IMS program in Singapore. It contains results on randomness, including answers to some open questions in higher randomness. There are structural results on equivalence relations,…
The 2012 logic blog has focussed on the following: Randomness and computable analysis/ergodic theory; Systematizing algorithmic randomness notions; Traceability; Higher randomness; Calibrating the complexity of equivalence relations from…
The logic blogs 2023 and 2024 have been joined. The present file contains a lot on particular classes of groups and their relationship with logic, as well as entries on ergodic theory and on foundations. There is also a bit on AI proving at…
Some notions from algorithmic randomness are extended to measures and to quantum states. There is a lot on group theory and its relation to logic. This includes some new results on oligomorphic groups. There's also metric spaces and Scott…
This year's logic blog has focussed on: 1. Demuth randomness 2. traceability 3. The connection of computable analysis and randomness 4. $K$-triviality in metric spaces.
This year's blog has focused on the connections of group theory with logic and algorithms. The first post is on automata presentable groups. Then there are several posts related to topological groups, for instance Ivanov and Majcher showing…
We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log2$, and $\pi^2$, their connection with already known ones, and underlying "permutation group" structures. Our principal arithmetic achievement…
In a recent volume of Mathematics Magazine (Vol. 90, No. 3, June 2017) there is an interesting article by Seth Zimmerman, titled Detecting Deficiencies: An Optimal Group Testing Algorithm. The claim in the summary is contradictory to…
We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if $\log r / \log s$ is irrational and $X$ and $Y$ are $\times r$- and $\times s$-invariant subsets of $[0,1]$, respectively,…
The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation.…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
This article discusses the logical errors in the liar paradox, G\"odel's incompleteness theorems, Russell's paradox, and the halting problem. In order to avoid these errors, a redefinition of logic has been presented, which is concluded as…
In a recent work [JNT \textbf{129}, 2154 (2009)], Gun and co-workers have claimed that the number $\,\log{\Gamma(x)} + \log{\Gamma(1-x)}\,$, $x$ being a rational number between $0$ and $1$, is transcendental with at most \emph{one} possible…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…