People
Zachary Faubion
Lecturer
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
BromfieldPearson
Room 105
Medford, MA 02155
Email @tufts.edu:
zachary.faubion
Phone: 6176272352
Expertise:
Set Theory, specifically forcing elementary embeddings and large cardinal axioms
Research:
In 1930 Gödel proved his famous Incompleteness Theorem showing that any
reasonable system in which to do mathematics is incapable of answering all
mathematical questions. Because of this insight the process of discovering,
cataloging and comparing independent statements has become an active area of
research. I study statements which can not be proven true or false from a given axiom system.
Some of the questions to I try to answer about such statements are:
 Is that statement relatively consistent with ZFC (and can we prove it is?)
 What is the consistency strength of the statement (i.e what additional
axioms must we add to ZFC in order to prove it is relatively consistent?)
 What does it imply if assumed to be true?
 What other undecidable statements are consistent/inconsistent with the statement?
 Most recently I have been examining the consistency strength of stationary
set reflection at successors of singular cardinals, for instance \( \aleph_{\omega+1}\).
My research makes heavy use of large cardinal properties, elementary embeddings and forcing.
