Calendar

Sep
26
Thu
Section 7.5
Sep 26 @ 10:30 am – 11:30 am
Oct
1
Tue
Midterm 1 MATH 307
Oct 1 @ 9:00 am – 10:00 am
Midterm 1 MATH 252A
Oct 1 @ 10:30 am – 11:30 am
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) ug(v) + u – 1.

Oct
3
Thu
Section 2.5
Oct 3 @ 9:00 am – 10:00 am
Section 7.7
Oct 3 @ 10:30 am – 11:30 am
Oct
8
Tue
Section 5.1
Oct 8 @ 9:00 am – 10:00 am
Section 7.8
Oct 8 @ 10:30 am – 11:30 am
Section 8.5
Oct 8 @ 10:30 am – 11:30 am
Oct
9
Wed
Logic seminar
Oct 9 @ 2:30 pm – 3:30 pm
Oct
10
Thu
Section 5.1/5.2
Oct 10 @ 9:00 am – 10:00 am
Section 9.1
Oct 10 @ 10:30 am – 11:30 am
Oct
15
Tue
Section 5.2
Oct 15 @ 9:00 am – 10:00 am
Section 9.2
Oct 15 @ 10:30 am – 11:30 am
Oct
16
Wed
Logic seminar: Jack Yoon
Oct 16 @ 2:30 pm – 3:30 pm


Assessing the Reverse Mathematical Strength of Gratzer-Schmidt Theorem
Gratzer-Schmidt theorem in lattice theory states that all complete and compactly generated lattices are isomorphic to the congruence lattice of an algebra. There has been an effort to assess the strength of this theorem in the reverse mathematical setting. I will discuss my recent progress on this topic and its potential implications.

Oct
17
Thu
Section 5.3
Oct 17 @ 9:00 am – 10:00 am
Section 9.3
Oct 17 @ 10:30 am – 11:30 am
Oct
22
Tue
Section 5.3/5.4
Oct 22 @ 9:00 am – 10:00 am
Section 9.4
Oct 22 @ 10:30 am – 11:30 am
Oct
23
Wed
Logic seminar: Jack Yoon (II)
Oct 23 @ 2:30 pm – 3:30 pm
Oct
24
Thu
Section 5.4
Oct 24 @ 9:00 am – 10:00 am
Section 9.5
Oct 24 @ 10:30 am – 11:30 am
Oct
29
Tue
Section 5.5
Oct 29 @ 9:00 am – 10:00 am
Section 10.1
Oct 29 @ 10:30 am – 11:30 am
Oct
30
Wed
Logic seminar: Kameryn Williams
Oct 30 @ 2:30 pm – 3:30 pm

I will speak about the recent paper “Condensable models of set theory” by Ali Enayat. The abstract can be found here: https://arxiv.org/abs/1910.04029

Oct
31
Thu
Section 5.5
Oct 31 @ 9:00 am – 10:00 am
Section 10.2
Oct 31 @ 10:30 am – 11:30 am
Section 10.3
Oct 31 @ 10:30 am – 11:30 am
Nov
5
Tue
Section 5.6
Nov 5 @ 9:00 am – 10:00 am
Section 10.4
Nov 5 @ 10:30 am – 11:30 am