TITLE: In Peter Smith's "Introduction to Gödel's Theorems," why are so many properties characterized as "effectively"
QUESTION [6 upvotes]: In "Introduction to Gödel's Theorems," the adverb "effectively" is almost ubiquitous: effectively enumerable, effectively decidable, effectively computable, etc.
Here are some sample quotes:


A property/relation is effectively decidable iff there is an algorithmic procedure...
A numerical property or relation is effectively decidable iff its characteristic function is effectively computable.
A one-place total function $f:\Delta\rightarrow \Gamma$ is effectively computable iff there is an algorithm...
There is an effectively enumerable set of numbers $K$ such that is compliment $\bar{K}$ is not effectively ennumerable.
for a properly formalized syntax $\mathcal{L}$, there should be clear and objective procedures...for effectively deciding whether a putative constant-symbol really is a constant...


Why can't one just state the feature or property without any modification?
Thanks

REPLY [6 votes]: Henning, Bram and Carl are of course right that my "effectively" is mostly for emphasis, to highlight the kind of decision procedures, enumerations, axiomatisations etc. are in question. 
We are, for example, concerned with what is effectively decidable -- i.e. decidable by a plodding finite step-by-step algorithmic procedure (so we want to emphasize that appeal to oracles, or to infinitary processes of hypercomputation, or anything exotic is like is ruled out as a "decision" procedure of the sort we care about).
We are, for example, concerned with what is effectively enumerable -- i.e. what can in effect by listed by a plodding finite step-by-step algorithmic procedure (so we want to emphasize that not any old function from numbers to widgets is enough to list the widgets in the way we are want to get at).
We are, for example, concerned with effectively axiomatized theories -- i.e. theories where it is effectively decidable what's an axiom (so we want to emphasize that not any old bunch of axioms will do for the sort of theories we are concerned with).
And so it goes. It could be that I overdid the repetitious use of "effectively". However -- without doing a careful re-read of the chapter -- my guess would be that it was indeed probably better to err on the side of being explicitly repetitious!