5 citations · 11 across the 18 of their papers we have counts for
22 papers
Word automatic groups of nilpotency class 2
Andre Nies, Frank Stephan
We consider word automaticity for groups that are nilpotent of class and have exponent a prime . We show that the infinitely generated free group in this variety is not word…
Logic Blog 2022
Andre Nies
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 connectio…
Logic Blog 2021
Andre Nies
The blog has several entries on group theory interacting with computability and wider logic, several open questions, and an entry on undecidability in physics.
Computable topological abelian groups
Martino Lupini, Alexander Melnikov, Andre Nies
We study the algorithmic content of Pontryagin - van Kampen duality. We prove that the dualization is computable in the important cases of compact and locally compact totally disco…
Logic Blog 2020
Andre Nies
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…
Logic Blog 2019
Andre Nies
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 char…
Finite axiomatizability for profinite groups
Andre Nies, Dan Segal, Katrin Tent
A group is (FA) in a class if it can be determined up to isomorphism within by a sentence in the first-order language…
The Scott rank of Polish metric spaces
Sy Friedman, Katia Fokina, Martin Koerwien +1
We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational , there is a relation $R_…
Logic Blog 2018
Andre Nies
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…
Logic Blog 2017
Andre Nies
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, descri…
The complexity of topological group isomorphism
Alexander S. Kechris, Andree Nies, Katrin Tent
We study the complexity of the isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducib…
Logic Blog 2016
Andre Nies
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…
Calibrating word problems of groups via the complexity of equivalence relations
André Nies, Andrea Sorbi
(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable…
The complexity of isomorphism between countably based profinite groups
Andre Nies
A topological group G is profinite if it is compact and totally disconnected. Equivalently, G is the inverse limit of a surjective system of finite groups carrying the discrete top…
Logic Blog 2015f
Andre Nies
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. The…
A Universal Separable Diversity
David Bryant, André Nies, Paul Tupper
The Urysohn space is a separable complete metric space with two fundamental properties: (a) universality: every separable metric space can be isometrically embedded in it; (b) ultr…
Logic Blog 2014
Andre Nies
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 randomne…
Superhighness
André Nies, Bjørn Kjos-Hanssen
We prove that superhigh sets can be jump traceable, answering a question of Cole and Simpson. On the other hand, we show that such sets cannot be weakly 2-random. We also study the…
Logic Blog 2011
André Nies
This year's logic blog has focussed on: 1. Demuth randomness 2. traceability 3. The connection of computable analysis and randomness 4. -triviality in metric spaces.
Logic Blog 2013
André Nies
The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of randomness and higher weak 2 randomness is determined. 2. Rev…
Logic Blog 2012
Andre Nies
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 Delta 2 sets via their changes
Andre Nies
The computational complexity of a Delta 2 set will be calibrated by the amount of changes needed for any of its computable approximations. Firstly, we study Martin-Loef random sets…