Thomas J. Jech ( cs, Tomáš Jech, ; born January 29, 1944 in
Prague
Prague ( ; cs, Praha ; german: Prag, ; la, Praga) is the capital and largest city in the Czech Republic, and the historical capital of Bohemia. On the Vltava river, Prague is home to about 1.3 million people. The city has a temperate ...
) is a
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
specializing in
set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...
who was at
Penn State for more than 25 years.
Life
He was educated at
Charles University
)
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, established =
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, budget = 8.9 billion CZK
, rector = Milena Králíčková
, faculty = 4,057
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, students = 51,438
, under ...
(his advisor was
Petr Vopěnka
Petr Vopěnka (16 May 1935 – 20 March 2015) was a Czech mathematician. In the early seventies, he developed alternative set theory (i.e. alternative to the classical Cantor theory), which he subsequently developed in a series of articles and m ...
) and from 2000 is at th
Institute of Mathematicsof the
Academy of Sciences of the Czech Republic
The Czech Academy of Sciences (abbr. CAS, cs, Akademie věd České republiky, abbr. AV ČR) was established in 1992 by the Czech National Council as the Czech successor of the former Czechoslovak Academy of Sciences and its tradition goes back ...
.
Work
Jech's research also includes
mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of forma ...
,
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary ...
,
analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...
,
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
, and
measure theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simila ...
.
Jech gave the first published proof of the consistency of the existence of a
Suslin line In mathematics, Suslin's problem is a question about totally ordered sets posed by and published posthumously.
It has been shown to be independent of the standard axiomatic system of set theory known as ZFC: showed that the statement can neit ...
.
With
Karel Prikry, he introduced the notion of
precipitous ideal. He gave several models where the
axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collection ...
failed, for example one with ω
1 measurable
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simila ...
. The concept of a
Jech–Kunen tree is named after him and
Kenneth Kunen.
Bibliography
*
* ''Lectures in set theory, with particular emphasis on the method of forcing'', Springer-Verlag Lecture Notes in Mathematics 217 (1971) ()
* ''The axiom of choice'', North-Holland 1973 (Dover paperback edition )
* (with K. Hrbáček) ''Introduction to set theory'', Marcel Dekker, 3rd edition 1999 ()
* ''Multiple forcing'', Cambridge University Press 1986 ()
''Set Theory'': The Third Millennium Edition, revised and expanded 2006, Springer Science & Business Media, . 1st ed. 1978;
2nd (corrected) ed. 1997
References
External links
Home page with a copy a
Penn state
*
{{DEFAULTSORT:Jech, Thomas
1944 births
Living people
20th-century Czech mathematicians
21st-century Czech mathematicians
Set theorists
Czechoslovak mathematicians