The shortest possible length of the longest implicational axiom (Q1914373)
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: The shortest possible length of the longest implicational axiom |
scientific article; zbMATH DE number 885305
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The shortest possible length of the longest implicational axiom |
scientific article; zbMATH DE number 885305 |
Statements
The shortest possible length of the longest implicational axiom (English)
0 references
6 January 1997
0 references
This interesting paper shows that every complete set of axioms of classical implicational logic (IF) must have at least one axiom of length 11 (in Polish notation). The matrix methods employed by the author also allow a simple proof of the Wajsberg/Diamond-McKinsley Theorem that every complete set of axioms must include at least one containing occurrences of 3 or more distinct propositional variables. Both results are ``best possible'' and also apply to all commonly used subsystems of IF.
0 references
shortest axioms
0 references
classical implicational logic
0 references
matrix methods
0 references
Wajsberg/Diamond-McKinsley theorem
0 references
