Introduction to clarithmetic II

The earlier paper “Introduction to clarithmetic I” constructed an axiomatic system of arithmetic based on computability logic, and proved its soundness and extensional completeness with respect to polynomial time computability. The present paper elaborates three additional sound and complete systems in the same style and sense: one for polynomial space computability, one for elementary recursive time (and/or space) computability, and one for primitive recursive time (and/or space) computability.

Authors

• Giorgi Japaridze

Keywords

• Computability logic
• Game semantics
• Peano arithmetic
• Constructive theories
• Interactive computation
• Bounded arithmetic
• Implicit computational complexity