FOM: technical questions on second-order logic

Stephen G Simpson simpson at
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?

-- Steve

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