An Interpretation of Robinson Arithmetic in its Grzegorczyk's Weaker Variant

Q− is a weaker variant of Robinson arithmetic Q in which addition and multiplication are partial functions, i.e. ternary relations that are graphs of possibly non-total functions. We show that Q is interpretable in Q− . This gives an alternative answer to a question of A. Grzegorczyk whether Q− is essentially undecidable.

• Type: Journal
• Year: 2007
• Where: FUIN
• Authors: Vítezslav Svejdar
• Keywords: FUIN 2007, Partial Functions, Robinson Arithmetic, Weaker Variant