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From High School to University Algebra Thorsten Altenkirch
 

Summary: From High School to University Algebra
Thorsten Altenkirch
1 Introduction
Wilkie showed that there are identities in Tarski's Highschool Algebra which are
not provable from the laws. At the core of his counterexample is the observation
that AD = BC implies
(Ay
+ By
)x
(Cx
+ Dx
)y
= (Ax
+ Bx
)y
(Cy
+ Dy
)x
but this is unprovable with the laws. Di Cosmo et al observed that this identity
corresponds to an isomorphism present in all bicartesian closed categories, i.e.

  

Source: Altenkirch, Thorsten - School of Computer Science, University of Nottingham

 

Collections: Computer Technologies and Information Sciences