Unless otherwise noted, all seminar meetings are on Thursdays at 4:00PM in Room 901 Van Vleck. Cookies and juice precede starting at about 3:45PM.
- Thursday, 19 January 2006: Alex Raichev on "Earn a
Math Ph.D. from One of Over 1500 Accredited Universities in Just 10
Easy Steps"
- Thursday, 26 January 2006: Will not meet - SWLC (Carl Mummert)
- Thursday, 2 February 2006: Asher Kach on "Atoms: The Building Blocks
of Nature (and Boolean Algebras) [Part I]"
- Thursday, 9 February 2006: Asher Kach on "Atoms: The Building Blocks
of Nature (and Boolean Algebras) [Part II]"
- Thursday, 16 February 2006: Will not meet
- Thursday, 23 February 2006: David Milovich on "A Problem of van
Douwen"
- Thursday, 2 March 2006: Paul Pedersen on "Completeness for Continuous
First-Order Logic"
- Thursday, 9 March 2006: Will not meet (Spring Break)
- Thursday, 16 March 2006: Will not meet (Spring Break)
- Thursday, 23 March 2006: Ali Godjali on "Non Well Founded Set Theory"
(AT 4:30PM)
- Thursday, 30 March 2006: TBA
- Thursday, 6 April 2006: James Hunter on "Continuity in Reverse Math
of Higher-Order Types"
- Thursday, 13 April 2006: Chris Alfeld on "The Medvedev Lattice of
Pi01 Classes in Not Heyting Algebra and Related Results"
- Thursday, 20 April 2006: TBA
- Thursday, 27 April 2006: GSCL7 Organizational Meeting
- Thursday, 4 May 2006: TBA
- Earn a Math Ph.D. from One of Over 1500 Accredited Universities in Just 10 Easy Steps (Alex Raichev): A full-proof strategy guaranteed to work or your money back. Presented by the beloved and distinguished B.Q. Bangwhistle, Board of Regents, University of California at Pennsylvania, Springfield, Hawaii.
- Atoms: The Building Blocks of Nature (And Boolean Algebras) [Part I] (Asher Kach): Unlike in nature, atoms are really the smallest objects in the field of Boolean algebras. After quickly discussing what an atom is, we'll move up to 1-atoms, 2-atoms, and the like. As time permits, we'll explore formulas in first-order logic that describe an atom, a 1-atom, and a 2-atom. Using these, we'll build (via a very simple infinite injury agrument) a computable Boolean algebra based on a non-computable predicate.
- Atoms: The Building Blocks of Nature (And Boolean Algebras) [Part II] (Asher Kach): After quickly reviewing the basics of Boolean algebras and the infinite injury argument from last week, we'll move on to slightly more sophisticated constructions. In addition to splitting the countable atomless Boolean algebra from countable algebras with atoms, we'll learn to split algebras containing only atoms from those containing 1-atoms using a moving marker construction.
- A Problem of van Douwen (David Milovich): Is there a homogeneous compact hausdorff space with a greater-than-continuum sized family of pairwise disjoing open subsets? Known as van Douwen's problem, this question is open in all models of set theory. The basic partial results for this problem will surveyed, followed by analogs of van Douwen's problem for some order-theoretic base properties.
- Completeness of Continuous First-Order Logic (Paul Perderson): In this talk, we show that continuous first-order logic is complete in the sense that a set of formulae is consistent only if it is (completely) satisfiable. We conclude with two corollaries: (i) an approximated form of strong completeness and (ii) compactness.
- Non-Well Founded Set Theory (Ali Godjali): Motivated by Jon Barwise's AMS talk on Non Well Founded Set Theory and Its Application, we will go over the basic definition and set up of Peter Aczel's Anti Foundation Axiom or AFA via pointed directed graph. The treatment here follows Keith Devlin's "The Joy of Sets". The talk ends with an analogy between non well founded sets and complex numbers.
- The Medvedev Lattice of Pi01 Classes in Not Heyting Algebra and Related Results (Chris Alfeld): For a distributive lattice define $a \rightarrow b$ to be the least $c$ such that $b \leq a \vee c$. A lattice is a Brouwer algebra if $a \rightarrow b$ always exists. A lattice is a Heyting algebra if its dual is a Brouwer algebra. I will show a recent result of Terwijn that the Medvedev Lattice of Pi01 Classes (in $\omega^\omega$) is not a Heyting algebra along with background and related results.