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   Turing-computable   numeric
functions. Yuri Gurevich's Abstract  State Machine Theorem states that every classical algorithm  is emulated (step for step)  by an abstract
state  machine,   which  is  a   most  generic  model   of  sequential
computation.  That theorem  presupposes three natural postulates about algorithmic  computation.  By  augmenting  those  postulates  with  an
additional   requirement  regarding   basic   operations,  a   natural
axiomatization of computability and a proof of Church’s Thesis obtain, as Gödel and others suggested may be possible.

Bio: http://www.math.tau.ac.il/~nachumd/Homepage.html

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