A Natural Axiomatization of Computability and Proof of Church's Thesis

Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turingle numeric functions. The Abstract State Machine Theorem states that every l algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's Thesis, as G

• Type: Journal
• Year: 2008
• Where: BSL
• Authors: Nachum Dershowitz, Yuri Gurevich
• Keywords: Abstract State Machine, BSL 2008, Numeric Functions, Turingle Numeric Functions