. Don Monk

Don Monk

My present research interests are the theory of infinite Boolean algebras and related set-theoretic topics, such as continuum cardinals and pcf theory. My previous research was in algebraic logic (cylindric algebras and relation algebras), and I also did some work in pure logic, set theory, and universal algebra. The files below are in postscript or pdf form, gzipped, tarred if several files are combined.
Boolean algebra bibliography (updated monthly, roughly)
Recent Research:
[63] Problems in the set theory of Boolean algebras. Mathematica Japonica 42, 1995, 179--185.
[64] Minimum-sized infinite partitions of Boolean algebras. Mathematical Logic Quarterly 42, 1996, 537--550.
[65] (with A. Dow) Depth, $\pi$-character, and tightness in superatomic Boolean algebras. Topology and its Applications 75, 1997, 183--199. There is a Correction to this.
[66] (with P. Nyikos) On cellularity in homomorphic images of Boolean algebras. Topology Proceedings 22, 1998, 341--362.
[67] The spectrum of partitions of a Boolean algebra. Archive for Mathematical Logic 40 (2001), 243--254.
[68] Generalized free products. Colloquium Mathematicum 88 (2001), 175--192.
[69] Continuum cardinals generalized to Boolean algebras. J. Symb. Logic 66 (2001), 1928--1958.
[70] An introduction to cylindric set algebras (with an appendix by H. Andreka. Logic Journal of the IGPL 8 (2000), 451--506. (Reprint, with corrections and an added appendix, of [62].)
[71] Boolean algebras. Entry in Stanford Encyclopedia of Philosophy (electronic) (2002); link to the Encyclopedia.
[72] An atomless interval Boolean algebra $A$ such that ${\frak a}(A)<{\frak t}(A)$.} Alg. Univ. 47 (2002), 495--500.
[73] The spectrum of maximal independent subsets of a Boolean algebra. Annals of Pure and Appl. Logic 126 (2004), 335--348.
[74] (with R. McKenzie) On some small cardinals for Boolean algebras. J. Symb. Logic 69 (2004), no. 3, 674--682.
[75] Generalized ${\frak b}$ and ${\frak d}$. Notre Dame J. Formal Logic 45 (2004), no. 3, 129--146.
[76] The size of maximal almost disjoint families. Dissert. Math. 437, 47pp. Inst. of Math., Polish Acad. Sci. (2006)
[77] Towers and maximal chains in Boolean algebras. Alg. Univ. 56 (2007), 337--347.
[78] Maximal irredundance and maximal ideal independence in Boolean algebras. J. Symb. Logic 73, no. 1 (2008), 261-275.
[79] On the existence of towers in pseudo-tree algebras. Order 26 (2009), 163-175.
[80] Leon Albert Henkin (1921--2006).} Bull. Symb. Logic 15, no. 3 (2009), 326-331.
[81] Special subalgebras of Boolean algebras. Math. Logic Quarterly 56, no. 2 (2010), 148-158.
[82] Maximal free sequences in a Boolean algebra. Comment. Math. Univ. Carol. 52, 4 (2011), 593--611.
[83] Remarks on continuum cardinals on Boolean algebras. Math. Log. Quarterly 58, no. 3 (2012), 159-167.
[84] Cardinal invariants on Boolean algebras. Second revised edition. (2014) vii + 573pp.
[85] Leon Henkin and cylindric algebras. In "The Life and Work of Leon Henkin.", Birkhauser, 59-66.
Lecture notes, etc.:
(1) Unpublished notes on subalgebras of interval algebras.
(2) Continuum cardinals
(3) Basic pcf theory. (files are put in a subdirectory "tmp")
(4) Notes on Cardinal invariants on Boolean algebras, second revised edition.
(5) Lectures on set theory
(6) Problems on cardinal functions on Boolean algebras
math 4000/5000
Calculus III