Calendar

Mar
24
Sun
Mariya Soskova
Mar 24 @ 10:30 am – 10:50 am
Aug
28
Wed
Logic Seminar: Kameryn Williams, Initial segments of models of set theory fixed pointwise by automorphisms
Aug 28 @ 2:30 pm – 3:30 pm

I will present on the paper “Largest initial segments pointwise fixed by automorphisms of models of set theory” by Enayat, Kaufmann, and McKenzie.

https://arxiv.org/abs/1606.04002

Keller Hall 301

Sep
4
Wed
Logic Seminar: Kameryn Williams, Initial segments of models of set theory fixed pointwise by automorphisms
Sep 4 @ 2:30 pm – 3:30 pm

I will present on the paper “Largest initial segments pointwise fixed by automorphisms of models of set theory” by Enayat, Kaufmann, and McKenzie.

https://arxiv.org/abs/1606.04002

Keller Hall 301

Sep
11
Wed
Logic seminar: David Webb
Sep 11 @ 2:30 pm – 3:30 pm
Sep
18
Wed
Logic seminar: David Webb
Sep 18 @ 2:30 pm – 3:30 pm

“Iterated ultrapowers for the masses”, part 2

Sep
25
Wed
Logic seminar: Mojtaba Moniri
Sep 25 @ 2:30 pm – 3:30 pm

Comparing Near-linearity Notions in Open Induction

There have been works in number theory on characterizing the class of Beatty sequences (integer parts of natural multiples of a fixed nonnegative real slope). The same is true for the inhomogeneous case when a fixed intercept is added before taking the integer part. We consider some notions of multiplicative or additive near-linearity and elaborate on the extent to which they charecterize various such sequences. We show some implications from standard number theory carry over to Open Induction and some do not. [In a second talk we could relate this to the weak fragment allowing the standard integers as a direct summand of a model. That second talk would include two more multiplicative vs. additive topics, details to follow.]

Oct
2
Wed
Logic seminar: Mojtaba Moniri
Oct 2 @ 2:30 pm – 3:30 pm

Some additive vs. multiplicative issues in subrecursivity, maximality, and near-linearity

We deal with three topics around addition without or with multiplication.

We first present algorithms to compute a certain real, generating its Beatty sequence or base 2 expansion. The former calculates in integers with addition, in conjunction with the counting operator. The latter calculates in integers with addition and multiplication. Motivation comes from subrecursive reals.

Next, let F be an ordered field, D a maximal discrete subring of F, and G a maximal discrete additive subgroup of F. We point out that although there are examples where F has elements of infinite distance to D, it can never realize any gaps of G. If F is countable, then G can be constructed Delta^0_2 relative to F.

Finally we finish and extend the talk of last week by considering some nonstandard models M of weak arithmetic which have the integers as an additive direct summand. We present functions f and g from M to M whose value at a sum minus sum of values is always 0 or 1 yet for some x,y,u,v ≥ 1in M, we have f(xy) < xf(y) and g(uv) > ug(v) + u – 1.

Oct
9
Wed
Logic seminar
Oct 9 @ 2:30 pm – 3:30 pm