Publications in VIVO

Co-author Network

Monk, James Donald

Professor Emerita/Emeritus

Positions

Professor Emerita/Emeritus, Mathematics

Research Areas

Research

research overview

I work on classifying infinite Boolean algebras according to various cardinal-valued functions defined on them. Some important examples are the cellularity (supremum of the cardinalities of disjoint subsets of an algebra), independence, and small independence. Altogether I am considering about 50 such functions.

keywords

set theory of Boolean algebras

Publications

selected publications

book
- Cardinal Invariants on Boolean Algebras 1996
- Cardinal invariants on Boolean algebras. Ed. 142. 1996
- Algebraic logic. Ed. 54. 1991
- Cardinal functions on Boolean algebras 1990
- Handbook of Boolean algebras. Vol. 1 1989
- Handbook of Boolean algebras. Vol. 2 1989
- Handbook of Boolean algebras. Vol. 3 1989
- Cylindric algebras. Part I. Ed. 64. 1985
- Cylindric algebras. Part II. Ed. 115. 1985
- Cylindric set algebras. Ed. 883. 1981
- Mathematical logic 1976
- Cylindric algebras. Part I. With an introductory chapter: General theory of algebras 1971
- Introduction to set theory 1969
chapter
- Lectures on cylindric set algebras. 253-290. 1993
- Corrections for the books: Cylindric algebras [Part I, North-Holland, Amsterdam, 1971; MR0314620 (47 #3171); Part II, 1985; MR0781930 (86m:03095b)] by L. Henkin, Monk and A. Tarski, and Cylindric set algebras [Lecture Notes in Math., 883, Springer, Berlin, 1981; MR0639151 (84a:03078)] by Henkin, Monk, Tarski, H. Andréka and I. Németi. 719-722. 1991
- Remarks on the problems in the books: Cylindric algebras [Part I, North-Holland, Amsterdam, 1971; MR0314620 (47 #3171); Part II, 1985; MR0781930 (86m:03095b)] by L. Henkin, Monk and A. Tarski, and Cylindric set algebras [Lecture Notes in Math., 883, Springer, Berlin, 1981; MR0639151 (84a:03078)] by Henkin, Monk, Tarski, H. Andréka and I. Németi. 723-726. 1991
- Structure problems for cylindric algebras. 413-429. 1991
- Appendix on set theory. 1213-1233. 1989
- Automorphism groups. 517-546. 1989
- Endomorphisms of Boolean algebras. 491-516. 1989
- The number of Boolean algebras. 469-490. 1989
- Cardinal functions on Boolean algebras. 9-37. 1984
- Tree algebras and chains. 54-66. 1983
- Some problems in algebraic logic. 83-249. 1977
- On automorphism groups of Boolean algebras. 951-Vol. 10. 1975
- Connections between combinatorial theory and algebraic logic. 58-Vol. 9. 1974
- Model-theoretic methods and results in the theory of cylindric algebras. 238-250. 1965
conference proceeding
- On cellularity in homomorphic images of Boolean algebras. Topology Proceedings. 341-362. 1997
- Cylindric algebras and related structures. 105-121. 1974
journal article
- The 3rd International Conference on Boolean Algebra, Lattice Theory, Universal Algebra, Set Theory and Set-theoretical Topology-BLAST 2010. Order: a journal on the theory of ordered sets. 229-230. 2012
- Remarks on continuum cardinals on Boolean algebras. Mathematical Logic Quarterly. 159-167. 2012
- Maximal free sequences in a Boolean algebra. Commentationes Mathematicae Universitatis Carolinae. 593-610. 2011
- Special subalgebras of Boolean algebras. Mathematical Logic Quarterly. 148-158. 2010
- In Memoriam: Leon Albert Henkin 1921–2006. Bulletin of Symbolic Logic. 326-331. 2009
- On the Existence of Towers in Pseudo-Tree Algebras. Order: a journal on the theory of ordered sets. 163-175. 2009
- Maximal irredundance and maximal ideal independence in Boolean algebras. The Journal of Symbolic Logic. 261-275. 2008
- Towers and maximal chains in Boolean algebras. Algebra Universalis. 337-347. 2007
- The size of maximal almost disjoint families. Dissertationes Mathematicae. 1-47. 2006
- On some small cardinals for Boolean algebras. The Journal of Symbolic Logic. 674-682. 2004
- On General Boundedness and Dominating Cardinals. Notre Dame Journal of Formal Logic. 2004
- The spectrum of maximal independent subsets of a Boolean algebra. Annals of Pure and Applied Logic. 335-348. 2004
- An atomless interval Boolean algebra A such that $ mathfrak{a} (A) $ < $ mathfrak{t} (A) $. Algebra Universalis. 495-500. 2002
- Continuum cardinals generalized to Boolean algebras. The Journal of Symbolic Logic. 1928-1958. 2001
- The spectrum of partitions of a Boolean algebra. Archive for Mathematical Logic. 243-254. 2001
- Generalized free products. Colloquium Mathematicum. 175-192. 2001
- An introduction to cylindric set algebras. Logic Journal of the IGPL. 451-496. 2000
- Erratum to “Depth, π-character, and tightness in superatomic Boolean algebras” Topology and its Applications 75 (1997) 183–199. Topology and its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology. 121-121. 2000
- Depth, π-character, and tightness in superatomic Boolean algebras. Topology and its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology. 183-199. 1997
- Minimum-sized infinite partitions of Boolean algebras. Mathematical Logic Quarterly. 537-550. 1996
- Problems in the set theory of Boolean algebras. Mathematica Japonica. 179-185. 1995
- Pseudo-trees and Boolean algebras. Order: a journal on the theory of ordered sets. 359-374. 1992
- THE CONTRIBUTIONS OF TARSKI,ALFRED TO ALGEBRAIC LOGIC. The Journal of Symbolic Logic. 899-906. 1986
- REPRESENTABLE CYLINDRIC ALGEBRAS. Annals of Pure and Applied Logic. 23-60. 1986
- ON ENDOMORPHISM BASES. Algebra Universalis. 264-266. 1985
- CARDINALITY AND COFINALITY OF HOMOMORPHS OF PRODUCTS OF BOOLEAN-ALGEBRAS. Algebra Universalis. 38-44. 1984
- Independence in boolean algebras. Periodica Mathematica Hungarica. 269-308. 1983
- Homogeneous Boolean algebras with very nonsymmetric subalgebras.. Notre Dame Journal of Formal Logic. 1983
- Chains in Boolean algebras. Annals of Mathematical Logic. 137-175. 1982
- CYLINDRIC SET ALGEBRAS AND RELATED STRUCTURES. Lecture Notes in Mathematics. 1-129. 1981
- Some questions about Boolean algebras. Algebra Universalis. 220-243. 1980
- A very rigid Boolean algebra. Israel Journal of Mathematics. 135-150. 1980
- The number of rigid boolean algebras. Algebra Universalis. 207-210. 1979
- Omitting types algebraically. 101-105. 1978
- FREE SUBALGEBRAS OF COMPLETE BOOLEAN ALGEBRAS. Archiv der Mathematik. 113-115. 1977
- FREE SUBALGEBRAS OF COMPLETE BOOLEAN ALGEBRAS. Archiv der Mathematik. 113-115. 1977
- AUTOMORPHISM GROUPS OF DENUMERABLE BOOLEAN ALGEBRAS. Mathematische Annalen. 5-10. 1975
- AUTOMORPHISM GROUPS OF DENUMERABLE BOOLEAN ALGEBRAS. Mathematische Annalen. 5-10. 1975
- Some cardinal functions on algebras. Algebra Universalis. 76-81. 1975
- Some cardinal functions on algebras. II. Algebra Universalis. 361-366. 1975
- Construction of the reals via ultrapowers. Rocky Mountain Journal of Mathematics. 1973
- On the number of complete boolean algebras. Algebra Universalis. 365-368. 1972
- On the general theory of m-groups. Fundamenta Mathematicae. 233-244. 1971
- Provability with finitely many variables. Proceedings of the American Mathematical Society. 353-358. 1971
- On the Foundations of Set Theory. American Mathematical Monthly. 703-711. 1970
- On an algebra of sets of finite sequences. The Journal of Symbolic Logic. 19-28. 1970
- Completions of Boolean algebras with operators. Mathematische Nachrichten. 47-55. 1970
- On equational classes of algebraic versions of logic. I. Mathematica Scandinavica: ediderunt societates mathematicae Daniae Fenniae Islandiae Norvegiae Sveci. 53-71. 1970
- Nonfinitizability of classes of representable cylindric algebras. The Journal of Symbolic Logic. 331-343. 1969
- Nontrivial $germ m$-injective Boolean algebras do not exist. Bulletin of the American Mathematical Society. 526-527. 1967
- $m$-semigroups, and function representations. Fundamenta Mathematicae. 233-241. 1966
- Substitutionless predicate logic with identity. Archiv f�r Mathematische Logik und Grundlagenforschung. 102-121 (1965). 1965
- Additions to some results of Erdös and Tarski. Fundamenta Mathematicae. 335-343. 1964
- On representable relation algebras. Michigan Mathematical Journal. 207-210. 1964
- Singulary cylindric and polyadic equality algebras. Transactions of the American Mathematical Society. 185-205. 1964
- Representation theory for polyadic algebras. Fundamenta Mathematicae. 151-176. 1963
- On pseudo-simple universal algebras. Proceedings of the American Mathematical Society. 543-546. 1962
- On the representation theory for cylindric algebras. Pacific Journal of Mathematics. 1447-1457. 1961

Background

education and training

Ph.D., University of California-Berkeley 1961
M.A., University of California-Berkeley 1959
B.S., University of New Mexico - Gallup Branch 1956
B.A., University of Chicago 1951

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geographic focus

Czech Republic Country
Israel Country
Poland Country
Switzerland Country

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ORCID iD

http://orcid.org/0000-0001-9614-5615