[Alta-Logic] peripatetic seminar

[Pieter Hofstra]

Time: Wednesday, 2pm

Place: SS1253

Speaker: Richard Zach

Title and abstract:

First-order Gödel logics (joint work with Matthias Baaz and Norbert
Preining)

First-order Gödel logics are a family of infinite-valued logics where
the sets of truth values V are closed subsets of [0, 1] containing both
0 and 1. Different such sets V in general determine different Gödel
logics G_V (sets of those formulas which evaluate to 1 in every
interpretation into V). It is shown that G_V is axiomatizable iff V is
finite, V is uncountable with 0 isolated in V, or every neighborhood of
0 in V is uncountable. Complete axiomatizations for each of these cases
are given. The r.e. prenex, negation-free, and existential fragments of
all first-order Goedel logics are also characterized.

The plan for this week is to discuss the topological properties of Gödel
sets and to prove that the sets of validities of Gödel logics based on
countable Gödel sets are not recursively enumerable.