Andreas Blass
Encyclopedia
Andreas Raphael Blass is a mathematician, currently a professor at the University of Michigan
. He specializes in mathematical logic
, particularly set theory
, and theoretical computer science
.
Blass graduated from the University of Detroit, where he was a Putnam Fellow, in 1966 with a B.S. in physics
. He received his Ph.D.
in 1970 from Harvard University
, with a thesis on Orderings of Ultrafilters written under the supervision of Frank Wattenberg. Since 1970 he has been employed by the University of Michigan, first as a T.H. Hildebrandt Research Instructor (1970–72), then assistant professor (1972–76), associate professor (1976–84) and since 1984 he has been a full professor there.
for every vector space
is equivalent to the Axiom of Choice. He made important contributions in the development of the set theory of the reals
and forcing
.
Blass was the first to point out connections between game semantics
and linear logic
.
He has authored about 175 research articles in mathematical logic and theoretical computer science, including:
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
. He specializes in mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
, particularly set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, and theoretical computer science
Theoretical computer science
Theoretical computer science is a division or subset of general computer science and mathematics which focuses on more abstract or mathematical aspects of computing....
.
Blass graduated from the University of Detroit, where he was a Putnam Fellow, in 1966 with a B.S. in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
. He received his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1970 from Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, with a thesis on Orderings of Ultrafilters written under the supervision of Frank Wattenberg. Since 1970 he has been employed by the University of Michigan, first as a T.H. Hildebrandt Research Instructor (1970–72), then assistant professor (1972–76), associate professor (1976–84) and since 1984 he has been a full professor there.
Selected publications and results
In 1984 Blass proved that the existence of a basisBasis (linear algebra)
In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system"...
for every vector space
Vector space
A vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex...
is equivalent to the Axiom of Choice. He made important contributions in the development of the set theory of the reals
Set theory of the real line
Set theory of the real line is an area of mathematics concerned with the application of set theory to aspects of the real numbers.For example, one knows that all countable sets of reals are null, i.e. have Lebesgue measure 0; one might therefore ask the least possible size of a setwhich is not...
and forcing
Forcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique invented by Paul Cohen for proving consistency and independence results. It was first used, in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory...
.
Blass was the first to point out connections between game semantics
Game semantics
Game semantics is an approach to formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player, somewhat resembling Socratic dialogues or medieval theory of Obligationes. In the late 1950s Paul Lorenzen was the...
and linear logic
Linear logic
Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter...
.
He has authored about 175 research articles in mathematical logic and theoretical computer science, including: