Calendar

Sep
5
Wed
7th: 1.7-8 (demonstrate simulation in Sheets)
Sep 5 @ 12:30 pm – 1:30 pm
Sep
7
Fri
8th: presentation of 1.7-8 homework
Sep 7 @ 12:30 pm – 1:30 pm
Sep
10
Mon
9th: 2.1-2; Module 1; show room computer usage
Sep 10 @ 12:30 pm – 1:30 pm
Logic Seminar: Kameryn Williams
Sep 10 @ 2:30 pm – 3:20 pm

Title: A conceptual overview of forcing

Abstract: Paul Cohen—who visited UH Mānoa in the 1990s—introduced the method of forcing to prove that the failure of the continuum hypothesis is consistent with ZFC, the standard base axioms for set theory. Since then it has become a cardinal tool within set theory, being the main method for proving independence results and even enjoys use in proving ZFC results. In this talk I will give an introduction to forcing, focusing on the big picture ideas.

This talk is a sequel to my previous talk and a prequel to my next talk.

Sep
12
Wed
Substitute Barb Bruno (10th)
Sep 12 @ 12:30 pm – 1:30 pm
Sep
14
Fri
2.3-4 Sam Birns (11th)
Sep 14 @ 12:30 pm – 1:30 pm
Sep
17
Mon
12th MATH 372
Sep 17 @ 12:30 pm – 1:30 pm
Logic Seminar: Kameryn Williams
Sep 17 @ 2:30 pm – 3:20 pm

Title: Forcing as a computational process

Abstract: In this talk we will consider computable structure theoretical aspects of forcing. Given an oracle for a countable model of set theory $M$, to what extent can we compute information about forcing extensions $M[G]$? The main theorem I will present gives a robustly affirmative answer in several senses.

* Given an oracle for the atomic diagram of a countable model of set theory $M$, then for any forcing notion $\mathbb P \in M$ we can compute an $M$-generic filter $G \subseteq \mathbb P$.

* From the $\Delta_0$ diagram for $M$ we can moreover compute the atomic diagram of the forcing extension $M[G]$, and indeed its $\Delta_0$ diagram.

* From the elementary for $M$ we can compute the elementary diagram of the forcing extension $M[G]$, and this goes level by level for the $\Sigma_n$ diagrams.

On the other hand, there is no functorial process for computing forcing extensions.

* If ZFC is consistent then there is no computable procedure (nor even a Borel procedure) which takes as input the elementary diagram for a countable model $M$ of ZFC and a partial order $\mathbb P \in M$ and returns a generic $G$ so that isomorphic copies of the same input model always result in the same corresponding isomorphic copy of $G$.

This talk is a sequel to my previous talk. The work in this talk is joint with Joel David Hamkins and Russell Miller.

Sep
19
Wed
13th 2.5, 3.1
Sep 19 @ 12:30 pm – 1:30 pm
Sep
20
Thu
Office hour
Sep 20 @ 10:00 am – 11:00 am
Sep
21
Fri
14th: present 2.5, 3.1
Sep 21 @ 12:30 pm – 1:30 pm
Sep
24
Mon
15th: Midterm 1
Sep 24 @ 12:30 pm – 1:30 pm
Sep
26
Wed
16th: 3.2-3
Sep 26 @ 12:30 pm – 1:30 pm
Sep
28
Fri
17th: present 3.2-3, and work on Module 2
Sep 28 @ 12:30 pm – 1:30 pm
Oct
1
Mon
18th: 3.4-5
Oct 1 @ 12:30 pm – 1:30 pm
Oct
3
Wed
19th: Present 3.4-5
Oct 3 @ 12:30 pm – 1:30 pm
Oct
5
Fri
20th: 4.1-2; Module 2
Oct 5 @ 12:30 pm – 1:30 pm
Oct
8
Mon
21st: UHM TV and Poisson distribution
Oct 8 @ 12:30 pm – 1:30 pm
Oct
10
Wed
22nd: 4.3-4
Oct 10 @ 12:30 pm – 1:30 pm
Oct
12
Fri
Students present 4.3-4
Oct 12 @ 12:30 pm – 1:30 pm
Oct
15
Mon
24th: 4.5, 5.1
Oct 15 @ 12:30 pm – 1:30 pm
Oct
17
Wed
Students present
Oct 17 @ 12:30 pm – 1:30 pm
Oct
19
Fri
26th: 5.2-3
Oct 19 @ 12:30 pm – 1:30 pm
Oct
22
Mon
27th
Oct 22 @ 12:30 pm – 1:30 pm
Oct
24
Wed
28th: Discuss MATH course problems
Oct 24 @ 12:30 pm – 1:30 pm
Oct
26
Fri
Present MATH course problems
Oct 26 @ 12:30 pm – 1:30 pm
Oct
29
Mon
30th: Midterm 2
Oct 29 @ 12:30 pm – 1:30 pm
Logic seminar: The number of maximally complex languages
Oct 29 @ 2:30 pm – 3:30 pm

Speaker: B. Kjos-Hanssen (joint work with Lei Liu)
Abstract:
Campeanu and Ho (2004) stated that it is “very difficult” to compute the number $m_n$ of maximally complex languages (in a finite automata sense) consisting of binary words of length $n$. We show that $m_n=O_{i,n}$, the number of functions from $[2^i]$ to $[2^{2^{n-i}}]$ whose range contains $[2^{2^{n-i}}-1]$, for the least $i$ for which $O_{i,n}>0$. Here, $[a]=${1,…,a}.

Oct
31
Wed
31st: 6.1-2
Oct 31 @ 12:30 pm – 1:30 pm
Nov
2
Fri
Monique Chyba visits
Nov 2 @ 12:30 pm – 1:30 pm