Negative resolution to the $C^*$-algebraic Tarski problem

Christopher Schafhauser; Srivatsav Kunnawalkam Elayavalli

Negative resolution to the $C^*$-algebraic Tarski problem

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2503.10505 v2 pith:SOILXNM6 submitted 2025-03-13 math.OA math.GRmath.LO

Srivatsav Kunnawalkam Elayavalli , Christopher Schafhauser This is my paper · ORCID

classification math.OAmath.GRmath.LO

keywords algebraicalgebrasgroupnegativeproblemtarskianalogueapplication

verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments

abstract

We compute the $K_1$-group of ultraproducts of unital, simple $C^*$-algebras with unique trace and strict comparison. As an application, we prove that the reduced free group $C^*$-algebras $C^*_r(F_m)$ and $C^*_r(F_n)$ are elementarily equivalent (i.e., have isomorphic ultrapowers) if and only if $m = n$. This settles in the negative the $C^*$-algebraic analogue of Tarski's 1945 problem for groups.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Some remarks on decay in countable groups and amalgamated free products
math.GR 2025-09 conditional novelty 7.0 of 10

Subexponential decay (SD) is introduced as a weakening of rapid decay; permanence of SD/RD under amalgamated free products is proved with sharp distortion bounds, with applications to selflessness of reduced C*-algebras.

Pith tools