Thomas Jech

Thomas J. Jech (Czech: Tomáš Jech, pronounced [ˈtomaːʃ ˈjɛx]; born 29 January 1944 in Prague) is a mathematician specializing in set theory who was at Penn State for more than 25 years.

Life

Jech gave the first published proof of the consistency of the existence of a Suslin line. With Karel Prikry, he introduced the notion of precipitous ideal. He gave several models where the axiom of choice failed, for example one with ω₁ measurable. The concept of a Jech–Kunen tree is named after him and Kenneth Kunen.

"Non-provability of Souslin's hypothesis", Comment. Math. Univ. Carolinae, 8: 291–305, 1967, MR 0215729
Lectures in set theory, with particular emphasis on the method of forcing, Springer-Verlag Lecture Notes in Mathematics 217 (1971) (ISBN 978-3540055648)
The axiom of choice, North-Holland 1973 (Dover paperback edition ISBN 978-0-486-46624-8)
(with K. Hrbáček) Introduction to set theory, Marcel Dekker, 3rd edition 1999 (ISBN 978-0824779153)
Multiple forcing, Cambridge University Press 1986 (ISBN 978-0521266598)^[1]
Set Theory: The Third Millennium Edition, revised and expanded, 2006, Springer Science & Business Media, ISBN 3-540-44085-2. 1st ed. 1978;^[2] 2nd (corrected) ed. 1997

v t e Set theory
Overview	Set (mathematics)
Axioms	Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set Regularity Union Martin's axiom Axiom schema replacement specification
Operations	Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union
Concepts Methods	Almost Cardinality Cardinal number (large) Class Constructible universe Continuum hypothesis Diagonal argument Element ordered pair tuple Family Forcing One-to-one correspondence Ordinal number Set-builder notation Transfinite induction Venn diagram
Set types	Amorphous Countable Empty Finite (hereditarily) Filter base subbase Ultrafilter Fuzzy Infinite (Dedekind-infinite) Recursive Singleton Subset · Superset Transitive Uncountable Universal
Theories	Alternative Axiomatic Naive Cantor's theorem Zermelo General Principia Mathematica New Foundations Zermelo–Fraenkel von Neumann–Bernays–Gödel Morse–Kelley Kripke–Platek Tarski–Grothendieck
Paradoxes Problems	Russell's paradox Suslin's problem Burali-Forti paradox
Set theorists	Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

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