Ineffability

Speaker: 

Julian Eshkol

Institution: 

UC Irvine

Time: 

Monday, February 26, 2024 - 4:00pm to 5:20pm

Host: 

Location: 

RH 340

Ineffability

This is the first of series of seminars that surveys the results of ineffability and its use in forcing extensions.

The first talk will be about the results in Magidor's Thesis where the fundamental notions were introduced. 

 

Algorithmic Randomness

Speaker: 

Michael Hehman

Institution: 

UC Irvine

Time: 

Tuesday, February 20, 2024 - 11:00am to 12:30pm

Host: 

Location: 

440R

NOTE: Tuesday meeting

This is the last lecture in an introductory survey of the theory of algorithmic randomness. The primary question we wish to answer is: what does it mean for a set of natural numbers, or equivalently an infinite binary sequence, to be random? We will focus on three intuitive paradigms of randomness: (i) a random sequence should be hard to describe, (ii) a random sequence should have no rare properties, and (iii) a random sequence should be unpredictable, in the sense that we should not be able to make large amounts of money by betting on the next bit of the sequence. Using ideas from computability theory, we will make each of these three intuitive notions of randomness precise and show that the three define the same class of sets.

Algorithmic Randomness part III

Speaker: 

Michael Hehman

Institution: 

UC Irvine

Time: 

Monday, February 12, 2024 - 4:00pm to 5:30pm

Host: 

Location: 

RH 340 N

This is the third lecture in an introductory survey of the theory of algorithmic randomness. The primary question we wish to answer is: what does it mean for a set of natural numbers, or equivalently an infinite binary sequence, to be random? We will focus on three intuitive paradigms of randomness: (i) a random sequence should be hard to describe, (ii) a random sequence should have no rare properties, and (iii) a random sequence should be unpredictable, in the sense that we should not be able to make large amounts of money by betting on the next bit of the sequence. Using ideas from computability theory, we will make each of these three intuitive notions of randomness precise and show that the three define the same class of sets.

Algorithmic Randomness Part 2

Speaker: 

Michael Hehmann

Institution: 

UC Irvine

Time: 

Monday, January 29, 2024 - 4:00pm to 5:30pm

Host: 

Location: 

RH 340N

We give an introductory survey of the theory of algorithmic randomness. The primary question we wish to answer is: what does it mean for a set of natural numbers, or equivalently an infinite binary sequence, to be random? We will focus on three intuitive paradigms of randomness: (i) a random sequence should be hard to describe, (ii) a random sequence should have no rare properties, and (iii) a random sequence should be unpredictable, in the sense that we should not be able to make large amounts of money by betting on the next bit of the sequence. Using ideas from computability theory, we will make each of these three intuitive notions of randomness precise and show that the three define the same class of sets.

 

Algorithmic Randomness

Speaker: 

Michael Hehmann

Institution: 

UC Irvine

Time: 

Monday, January 22, 2024 - 4:00pm to 5:30pm

Host: 

Location: 

RH 340 N

We give an introductory survey of the theory of algorithmic randomness. The primary question we wish to answer is: what does it mean for a set of natural numbers, or equivalently an infinite binary sequence, to be random? We will focus on three intuitive paradigms of randomness: (i) a random sequence should be hard to describe, (ii) a random sequence should have no rare properties, and (iii) a random sequence should be unpredictable, in the sense that we should not be able to make large amounts of money by betting on the next bit of the sequence. Using ideas from computability theory, we will make each of these three intuitive notions of randomness precise and show that the three define the same class of sets.

 

Recent progress in the study of compactness phenomena

Speaker: 

Alejandro Poveda

Institution: 

Harvard University

Time: 

Monday, February 5, 2024 - 4:00pm to 5:30pm

Host: 

Location: 

RH 340 N

 This talk will be concerned with compactness phenomena in set theory. Compactness is the phenomenon by which the local properties of a mathematical structure determine its global behaviour. This phenomenon is intrinsic to the architecture of the mathematical universe and manifests in various forms. Over the past fifty years, the study of compactness phenomena has been one of the flagships of research in set theory. This talk will present recent discoveries spanning classical themes like the tree property and stationary reflection while also forging new connections with other topics, such as Woodin's HOD Conjecture.

Unreachability of $\Gamma_{2n+1,m}$

Speaker: 

Derek Levinson

Institution: 

UCLA

Time: 

Monday, November 27, 2023 - 4:00pm to 5:30pm

Host: 

Location: 

RH 340P

We prove from ZF + AD + DC that there is no sequence of distinct $\Gamma_{1,m}$ sets of length $\aleph_{m+2}$. This is the optimal result for the pointclass $\Gamma_{1,m}$ by earlier work of Hjorth. We also get a bound on the length of sequences of $\Gamma_{2n+1,m}$ sets using the same techniques.

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