Equational theory of positive numbers with exponentiation is not finitely axiomatizable (Q918968)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Equational theory of positive numbers with exponentiation is not finitely axiomatizable |
scientific article; zbMATH DE number 4160699
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equational theory of positive numbers with exponentiation is not finitely axiomatizable |
scientific article; zbMATH DE number 4160699 |
Statements
Equational theory of positive numbers with exponentiation is not finitely axiomatizable (English)
0 references
1990
0 references
The author considers the equational theory K of \((N,1,+,*,\uparrow).\) Let T be the standard axioms for addition, multiplication and exponentiation. A. Tarski asked if the whole of K can be derived from T. A. J. Wilkie first provided an identity holding in N but not derivable from T. It is proved in the paper that for any finite \(S\subseteq K\) there is an identity from K in one variable which is not derived from S.
0 references
positive numbers with exponentiation
0 references
finitely axiomatizable
0 references
equational theory
0 references
identity
0 references
0 references
