MOPA

Videos Playlist

Session 1 (11:00 AM - 1:30 PM):
11:00 - 11:05 Welcome
11:05 - 11:35 Angus Macintyre
11:40 - 12:10 Ali Enayat Slides
12:10 - 12:25 Coffee break
12:25 - 12:55 Ermek Nurkhaidarov
1:00 - 1:30 Stephen Simpson Slides

Session 2 (3:00 - 5:30 PM)
3:00 - 3:30 David Marker Slides
3:35 - 4:05 Manuel Lerman
4:05 - 4:20 Coffee break
4:20 - 4:50 Matt Kaufmann Notes
4:55 - 5:30 There is still work to be done.

I shall expound Michael Dummett's claim in his paper, 'The philosophical significance of Gödel's theorem' (1963), and in later writings, that a consequence of the indefinite extensibility of Gödel incompleteness is that 'the meaning of 'natural number' is inherently vague'. Though of course Gödel incompleteness establishes that every formal system containing basic arithmetic has a proper extension, I claim, against Dummett's view, that there is a notion of arithmetical truth intrinsic to the meaning of 'natural number' which is stable, not indefinitely extensible, and that first-order Peano Arithmetic is sound and complete with respect to that notion of arithmetical truth. Thereby the meaning of 'natural number' is not vague but clear and precise.

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In this talk we continue the discussion on the automorphism groups of countable short recursively saturated models of PA. In particular, we discuss the cuts of the model which are fixed setwise by all automorphisms (invariant cuts). We show that such cuts occur in different places of the model, depending on the types realized in the last gap. We then show that this implies, in some of these cases, that the automorphism groups of such models are non-isomorphic as topological groups. This is a joint work with Ermek Nurkhaidarov.

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In this talk we discuss automorphisms of countable short recursively saturated models of PA.

Kossak-Schmerl 95 shows that: if M is a countable, arithmetically saturated model of PA, then the automorphism group of M codes its standard system. We discuss how to prove a similar result for countable short arithmetically saturated models of PA.

This is joint work with Erez Shochat.

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