The first meeting of the logic seminar will be today at 2:30–3:20 in Keller 314. Our speaker will be Jack Yoon, who will give an introductory lecture on reverse mathematics. An abstract for his talk is below.
I will introduce the basics of reverse mathematics and begin Hunter’s paper on higher order reverse topology, which can be found here: https://www.math.wisc.edu/
Reverse mathematics is a study of foundations of mathematics by assessing the “strength” of the theorems from ordinary mathematics. Rather than starting from given axioms to prove a theorem, it asks a reverse question “which axioms are necessary to prove the theorem?”. Traditionally, reverse mathematics has played out within the second order arithmetic, but further progress has been made on higher order systems as well. For example, Hunter’s paper above branches out to higher order systems to study the theorems of topology.
The logic seminar today will be given by David Webb. A title and abstract are below.
Title: On The Levin-V’yugin Degrees
Abstract: I will define and discuss the Levin-V’yugin degrees, a measure algebra defined on collections of reals closed under Turing equivalence. Roughly speaking, in this ordering collections A and B have that A<B if for any probabilistic algorithm, the probability that it produces an element of A that is not in B is 0. Time permitting, I will prove that the computable reals and the random reals each form an atom in this Boolean algebra, and discuss other degrees and their positions in the lattice.
The paper this talk is based on is here: https://arxiv.org/pdf/1907.
Time and place: Tuesday September 14, 10:30am in Holmes 247.
Speaker: Ellen Hughes, undergraduate student, UH Manoa.
Title: The interest equation in Lean
Abstract: We discuss how to solve the equation $y=x(1+i)^n$ for $i$ and for $n$ in the Lean proof assistant.
This is joint work with Monica Johnson, Ryan Sasaki and Prof. Kjos-Hanssen.
Covid-19 mitigation plan:
Participants will be required to show vaccination or testing status using the Lumisight app upon entry, observe 3ft social distancing, and to wear masks throughout.
Hope to see you there.
Computing from a pair of oracles one of which is useful
Title: Introduction to Modal Logic: Filtrations and Finite Model Property of $S_5$
Abstract : We’ll introduce some basic notions from Modal Logic namely, Kripke Frames, Standard Models, Filtrations etc. Then we’ll demonstrate the Finite Model Property of the system $S_5$ and this will be our main goal.