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From: guttman@linus.mitre.org
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To: info-hol@clover.ucdavis.edu
Cc: jt@linus.mitre.org, farmer@linus.mitre.org
Subject: Semantics: Full or general?

I couldn't tell from the HOL paper in the Birtwistle/Subrahmanyam volume (I may
have missed it) whether the intended semantics for HOL is full or general in
the sense that Henkin gave.  That is, in the functional types in the hierarchy,
does a structure have to contain *all* possible functions between its range and
domain types?  Or may particular models have smaller sets of functions?

As another way of posing the question, consider the example of the Peano axioms
formulated in HOL:  are all models of this theory isomorphic?

        Josh


