Sofic profiles of $S(\omega )$ and computability

Abstract: We show that for every sofic chunk

E

there is a bijective homomorphism

f : E_{c} i g h t a r r o w E

, where

E_{c}

is a chunk of the group of computable permutations of

m a t h b b N

so that the approximating morphisms of

E

can be viewed as restrictions of permutations of

E_{c}

to finite subsets of

m a t h b b N

. Using this we study some relevant effectivity conditions associated with sofic chunks and their profiles.

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