相关论文: Logic Blog 2020
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 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 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 has several entries on group theory interacting with computability and wider logic, several open questions, and an entry on undecidability in physics.
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…
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…
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.
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…
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,…
This year's logic blog contains a variety of results, some of them available only here. Highlights include the resolution of the Gamma question by Monin, and a number of entries on topological group theory and its connection to logic.…
We study, in the context of algorithmic randomness, the closed amenable subgroups of the symmetric group $S_\infty$ of a countable set. In this paper we address this problem by investigating a link between the symmetries associated with…
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 is a semitutorial-style survey of computability logic. An extended online version of it is maintained at http://www.csc.villanova.edu/~japaridz/CL/ .
The concept of a C-approximable group, for a class of finite groups C, is a common generalization of the concepts of a sofic, weakly sofic, and linear sofic group. Glebsky raised the question whether all groups are approximable by finite…
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.…
I introduce modal group theory, in which we study the category of all groups, considering embeddability as providing a notion of modal possibility. Using HNN extensions and Britton's lemma, I demonstrate that the modal language of groups is…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new…