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.
Vita
Boolean algebra bibliography (updated monthly, roughly)
Recent Research; following the numbering of my vita:
[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.
[A] Maximal irredundance and maximal ideal independence. Submitted.
Lecture notes, etc.:
(1) Unpublished notes on subalgebras of interval algebras.
(2) A brief introduction to Boolean algebras
(3) Concerning problems about cardinal invariants on Boolean algebras
(4) Continuum cardinals
(5) Basic pcf theory. (files are put in a subdirectory "tmp")
Math 6730
Math 3140

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