Karel Hrbáček (born 1944) is professor emeritus of mathematics at City College of New York. He specializes in

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 formal ...

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 conce ...

, and

non-standard analysis The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta ...

Early life and education

Karel studied at Charles University with

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 ...

, looking at large

cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. T ...

s. He was awarded the degree RNDr. Before his appointment at CCNY he was an exchange fellow at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

and a research associate at Rockefeller University. In 1980 he received an award from the Mathematical Association of America for his article on Non-standard Set Theory.

Selected publications

* 1999: (with

Thomas Jech Thomas J. Jech ( cs, Tomáš Jech, ; born January 29, 1944 in Prague) is a mathematician specializing in set theory who was at Penn State for more than 25 years. Life He was educated at Charles University (his advisor was Petr Vopěnka) and from ...

) ''Introduction to Set Theory'', Third edition. Monographs and Textbooks in Pure and Applied Mathematics, 220. Marcel Dekker J. M. Henle (1985), Review of ''Introduction to set theory'', 2nd ed., . * 1992: (with David Ballard) "Standard foundations for nonstandard analysis",

Journal of Symbolic Logic The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by ''Mathematical Reviews'', Zentralb ...

57(2): 741–748 * 1979: "Nonstandard set theory", American Mathematical Monthly 86(8): 659–677 * 1978: "Axiomatic foundations for nonstandard analysis",

Fundamenta Mathematicae ''Fundamenta Mathematicae'' is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical sys ...

98(1): 1–19

References

{{DEFAULTSORT:Hrbacek, Karel Mathematical logicians Set theorists City College of New York faculty 1944 births Living people