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C00002 00002	.require "memo.pub[let,jmc]" source
C00004 00003	NOTES
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.require "memo.pub[let,jmc]" source;
.cb MINIMAL MODELS AND RELATED TOPICS


	Let ⊗M1 and ⊗M2 be two models of a set ⊗A of sentences,
and let ⊗B be another set of sentences.  We write

	%2M1 ≡ M2 (mod B)%1

if and only if

	%2∀p.(pεB ⊃ true(p,M1) ≡ true(p,M2))%1.

We will be interested in the equivalence classes of this equivalence
relation.
Sometimes they will be finite objects or finitely specifiable when
the models themselves are not.

The equivalence is usually non-trivial, because the axioms ⊗A often
contain facts irrelevant to the sentences of ⊗B.  This suggests
reducing the set of functions and predicates and rewriting the
axioms so that the new ⊗A' will have fewer models, and there
will again be one model per equivalence class.  I have no idea
under what conditions this can be done.
NOTES

1. ¬∃x.(x is wrong with the boat) ⊃ (the boat can be used to croos the river).
This allows us to use minimal models to jump to the conclusion that
the river can be crossed.

2. A sentence is minimally undetermined by ⊗A iff it is true in some
minimal models of ⊗A and false in others.

3. A set ⊗B of sentences is determined by a set ⊗A if the truth
values of all %3p ε B%1 are determined by ⊗A.