SATisfying the High School Identities but not Wilkie's Identity
2026-08-17 • Logic in Computer Science
Logic in Computer Science
AI summaryⓘ
The authors solved a long-standing math question about certain algebra rules called the High School Identities. They proved that you cannot have an algebra with 11 elements that follows these rules but breaks another specific rule called Wilkie's identity. To do this, they turned the problem into a type of puzzle called a SAT problem and double-checked their solution. They also found a new example with 12 elements that behaves differently from known examples. This work clarifies what kinds of small algebra systems can exist with these properties.
Tarski's High School Algebra problemHigh School IdentitiesWilkie's identityalgebracountermodelSAT solverisomorphismmathematical logic
Authors
Agon Hajdari, Johannes Niederhauser
Abstract
We settle an open question related to Tarski's High School Algebra problem by showing that no 11-element algebra can satisfy the High School Identities while refuting Wilkie's identity. We encode the search as a SAT instance and independently verify the result. As a byproduct, we obtain a new 12-element countermodel that is not isomorphic to the previously known one.