FOM: technical questions on second-order logic
Stephen G Simpson
simpson at math.psu.edu
Tue Mar 23 03:56:24 EST 1999
I'm getting tired of the discussion of so-called `second-order logic
with standard semantics', which appears to be going nowhere because of
fundamental misunderstandings on the part of some participants.
Let's try to turn this discussion in a positive direction. Maybe we
can make progress on understanding some technical questions.
1. Joe Shipman 15 Mar 1999 15:24:11 asked about the L"owenheim number
of second-order logic. Could someone please comment on that?
2. I asked a question about the axiom of choice, which arose from
Shapiro's book. (See 15 Mar 1999 19:45:37.)
3. Joe Shipman and I had an off-line discussion about correlating ZF
with rules of inference for second-order logic. Joe, could you please
summarize the current state of that discussion?
4. In response to some comments of Hayes, I asked about the pros and
cons of quantifiers versus lambda calculus etc in second-order logic.
There have been some postings about this by Mossakowski and Makarov,
but surely more can be said. First, could somebody please spell out a
system of second-order logic based on lambda calculus? Second, could
somebody please comment in more detail on the resolution method?
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