Re: Universe nonemptyness assumption and Truth valuations

On Jun 6, 12:03 am, malc...@xxxxxxxxx wrote:
On 5 jun, 21:16, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

Note: By the way, Shoenfield (you said you're using Shoenfield, I
think I recall) says 'valid in the model' (or something like that)
where many other authors (and I think more usually) say 'true in the
model'. So don't let that confuse you. His 'valid in the model' does
NOT mean what the other authors mean by a 'validity' or 'valid
formula', which is a formula that is satisfied (or true, if a
sentence) in EVERY model.

Shoenfield defines a formula to be valid in a structure if all the
meanings of the formula are true in the given structure.
By meaning he
understands what is also usually called interpretation, i. e.
assignments of elements of the universe to the variables, and by true
he understands true under the interpretation (via the standard
recursive definition).

I don't recall him using the word 'meanings'. But in any case, what
you just said is otherwise on the same lines as what I said. My point
is to warn that many other authors do not use 'valid' in Shoenfield's
(also, as I recall, Church too) so we have to be careful about that
partcular bit of terminology, to keep in mind that 'valid' in his
treatment does not mean the same as 'valid' in the treatment of many
other authors (arguably most authors, arguably standard as opposed to
Shoenfield's and Church's(?) use).

MoeBlee
.

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