1993/03/01 by Stanley Burris, Simon Lee · 18 citations
Mathematics · Computer Science · Medicine · #History and Theory of Mathematics #Computability, Logic, AI Algorithms #Mathematics and Applications #Mathematics #Mathematics education #Calculus (dental) #Pure mathematics #Medicine
paper · doi:10.1080/00029890.1993.11990393
published in American Mathematical Monthly 100(3), 231-236 (Taylor & Francis)
openalex publication_date 1993/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
An algebra <A, +, x, X, 1) which satisfies HSI is called an HSI-algebra; and an algebra <A, +, x , 1) which satisfies HSI is called an HSI-algebra. N is the HSI-algebra <N, +, x, 1, 1), where N is the set of positive integers, and +, x , T are the familiar operations of addition, multiplication and exponentiation; and N is the familiar HSI-algebra <N, +, x , 1). One is so accustomed to associating the identities HSI with the natural numbers that it is perhaps surprising to discover that (i) there are lots of finite HSI-algebras, and (ii) there are identities true of N which cannot be derived from HSI. The question of whether or not HSI provides a basis for all the identities of N has a history going back at least to the 1960s, and is called Tarski's High School Problem. The negative solution to this problem was first given in 1980 by Wilkie in [10] where he shows that the identity