Every linear order isomorphic to its cube is isomorphic to its square V

Speaker: 

Garrett Ervin

Institution: 

UCI

Time: 

Monday, April 11, 2016 - 4:00pm to 5:30pm

Host: 

Location: 

RH 440R

Building on our characterization from last week of the orders X that are isomorphic to AX, we characterize those X that are isomorphic to AAX. We then write down a condition -- namely, the existence of a parity-reversing automorphism (p.r.a.) for the countable power of A -- under which the implication ``AAX = X implies AX = X" holds. In future talks, we will show that if X is isomorphic to its cube then the countable power of X has a p.r.a., and hence X is isomorphic to its square.

 

Every linear order isomorphic to its cube is isomorphic to its square IV

Speaker: 

Garrett Ervin

Institution: 

UCI

Time: 

Monday, April 4, 2016 - 4:00pm to 5:30pm

Host: 

Location: 

RH 440R

We continue toward a proof of the main theorem by characterizing, for a fixed linear order A, the collection of linear orders X such that AX is isomorphic to X, finishing the argument we started with the last time.

Every linear order isomorphic to its cube is isomorphic to its square

Speaker: 

Garrett Ervin

Institution: 

UCI

Time: 

Monday, February 29, 2016 - 4:00pm to 5:30pm

Host: 

Location: 

RH 440R

In 1950's Sierpinski asked whether there exists a linear order X isomorphic to its lexicographicaly ordered cube but not to its square. We will give some historical context and begin the proof that the answer is negative. More generally, if X is isomorphic to any of its finite powers X^n (n>1) then X is isomorphic to all of them.

Guessing models

Speaker: 

Sean Cox

Institution: 

Virginia Commonwealth University

Time: 

Monday, January 4, 2016 - 4:00pm to 5:30pm

Host: 

Location: 

RH 440R

Many consequences of the Proper Forcing Axiom (PFA) factor through the stationarity of the class of guessing models. Such consequences include the Tree Property at $\omega_2$, absence of (weak) Kurepa Trees on $\omega_1$, and failure of square principles.  On the other hand, stationarity of guessing models does not decide the value of the continuum, even when one requires that the guessing models are also indestructible in some sense.  I will give an introduction to the topic and discuss some recent results due to John Krueger and me.

Perfect and Scattered Subsets of Generalized Cantor Space VII

Speaker: 

Geoff Galgon

Institution: 

UCI

Time: 

Monday, November 23, 2015 - 4:00pm to 5:30pm

Host: 

Location: 

RH 440R

We continue our discussion of perfect and scattered subsets in the generalized Cantor space. We give some properties of the \kappa-topologies over 2^{\lambda} introduced earlier (for \kappa \leq \lamba), define a Cantor-Bendixon process for forests, and begin work on showing the consistency of Cantor-Bendixon theorem analogues for closed subsets of 2^{\kappa} and P_{\kappa^+}\lambda, for \kappa regular.

 

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