- Email address:
**don....@colorado.edu (fill in the dots)**

Boolean algebra bibliography (updated monthly, roughly)

Publications:

[01] On the representation theory for cylindric algebras. Pacific J. Math. 11, 1961, 1447--1457.

[02] On pseudo-simple universal algebras. Proc. Amer. Math. Soc. 13, 1962, 543--546.

[03] (with A. Daigneault) Representation theory for polyadic algebras. Fund. Math. 52, 1963, 151--176.

[04] (with D. Scott) Additions to some results of Erd\"os and Tarski. Fund. Math. 53, 1964, 335--343.

[05] Singulary cylindric and polyadic algebras. Trans. Amer. Math. Soc. 112, 1964, 185--205.

[06] On representable relation algebras. Mich. Math. J. 11. 1964, 207--210.

[07] The substitutionless predicate logic. Archiv f. Math. Logik und Grundlagenforschung 7, 1964, 102--121.

[08] Model-theoretic methods and results in the theory of cylindric algebras. in The Theory of Models, Proc. of a Symposium. 1965, 238--250.

[09] (with F. M. Sioson) $m$-semigroups, semigroups, and function representations. Fund. Math. 59, 1966, 233--241.

[10] Non-trivial $m$-injective Boolean algebras do not exist. Bull. Amer. Math. Soc. 73, 1967, 526--527.

[11] Introduction to Set Theory, McGraw-Hill, 1969 , ix + 193pp; Italian translation: Introduzione alla teorioa degli insiemi, Boringhieri 1972, 241 pp.

[12] Nonfinitzability of classes of representable cylindric algebras. J. Symb. Logic 34, 1969, 331--343.

[13] On an algebra of sets of finite sequences. J. Symb. Logic 35, 1970, 19--28.

[14] On the foundations of set theory. Amer. Math. Monthly 77, 1970, 703--711.

[15] Completions of Boolean algebras with operators. Math Nachr. 46, 1970, 47--55.

[16] On equational classes of algebraic versions of logic, I. Math. Scand. 27, 1970, 53--71.

[17] (with L. Henkin, A. Tarski) {\bf Cylindric Algebras, Part I.} North--Holland, 1971 vi $+$ 508pp.

[18] Provability with finitely many variables. Proc. Amer. Math. Soc. 27, 1971, 353--358.

[19] (with F. M. Sioson) On the general theory of m-groups. Fund. Math. 72, 1971, 233--244.

[20] (with R. Solovay) On the number of complete Boolean algebras. Algebra Universalis 2, 1972, 365--368.

[21] (with G. Meisters) Construction of the reals via ultrapowers. Rocky Mountain J. Math. 3, 1973, 141--158.

[22] (with R. McKenzie) On automorphism groups of Boolean algebras. Proc. Erd\"os Symposium 1973, 951--988.

[23] Connections between combinatorial theory and algebraic logic. Algebraic Logic, Math. Assoc. Amer. 1974, 58--91.

[24] (with L. Henkin) Cylindric algebras and related structures. Proc. Symp. in honor of A. Tarski 1974, 105--122.

[25] Some cardinal functions on algebras. Algebra Universalis 5, 1975, 76--81.

[26] On the automorphism groups of denumerable Boolean algebras. Math. Ann. 216, 1975, 5--10.

[27] Some cardinal functions on algebras, II. Algebra Universalis 5, 1975, 361--366.

[28] Some problems in algebraic logic. Proc. Summer Logic Conf., Clermont--Ferrand, CNRS 49, 1975, 83--88.

[29] Mathematical Logic. Springer--Verlag, 1976 , x $+$ 531pp.

[30] On free subalgebras of complete Boolean algebras.} Arch. d. Math. 29, 1977, 113--115.

[31] Omitting types algebraically. Ann. Sci. Univ. Clermont, Ser. Math. Fasc. 16, 1978, 101--105.

[32] (with W. Rassbach) The number of rigid Boolean algebras. Algebra Universalis 9, 1979, 207--210.

[33] A very rigid Boolean algebra.} Israel J. Math. 35, 1980, 135--150.

[34] (with E. K. van Douwen, M. Rubin) Some questions about Boolean algebras. Algebra Universalis 11, 1980, 220--243.

[35] (with L. Henkin, A. Tarski, H. Andr\'eka, I. N\'emeti) Cylindric Set Algebras.} Springer-Verlag, Lecture Notes in Mathematics 883, 1981, 323pp.

[36] (with L. Henkin, A. Tarski) Cylindric set algebras and related structures . in {\bf Cylindric Set Algebras.} Springer--Verlag, Lecture Notes in Mathematics 883, 1981, 1--129.

[37] (with R. McKenzie) Chains in Boolean Algebras. Annals of Math. Logic 22, 1982, 137--175

[38] Independence in Boolean Algebras. Periodica Mathematica Hungarica 14, 1983, 269--308.

[39] (with S. Koppelberg) Homogeneous Boolean algebras with very nonsymmetric subalgebras. Notre Dame J. Formal Logic 24, 1983, 353--356.

[40] (with G. Brenner) Tree algebras and chains. in Springer Lecture Notes in Mathematics 1004, 1983, 54-66.

[41] (with B. Koppelberg, R. McKenzie) Cardinality and cofinality of homomorphs of products of Boolean algebras. Algebra Universalis 19, 1984, 38--44.

[42] Cardinal functions on Boolean algebras. Proc. Ordered Sets Conf., Orders: ~Descriptions and Roles, North--Holand 1984, 9--37.

[43] (with L. Henkin, A. Tarski) {Cylindric Algebras, Part II. North--Holland, 1985, 302pp.

[44] On endomorphism bases. Algebra Universalis 20, 1985, 264--266.

[45] (with L. Henkin, A. Tarski) Representable cylindric algebras. Ann. Pure Appl. Logic 31, 1986, 23--60

[46] Tarski's contributions to algebraic logic. J. Symb. Logic 51, 1986, 899--906.

[47] (editor, with the cooperation of R. Bonnet) Handbook of Boolean Algebras, vol. 1. North--Holland, 1989, xix + 312pp.

[48] (editor, with the cooperation of R. Bonnet) Handbook of Boolean Algebras, vol. 2. North--Holland, 1989, 313--716pp.

[49] (editor, with the cooperation of R. Bonnet) Handbook of Boolean Algebras, vol. 3. North--Holland, 1989, 717--1366pp.

[50] The number of Boolean algebras. in {\bf Handbook of Boolean algebras.} North--Holland, 1989, 469--489.

[51] Endomorphisms of Boolean algebras. in {\bf Handbook of Boolean algebras.} North--Holland, 1989, 491--516.

[52] Automorphism groups. in {\bf Handbook of Boolean Algebras.} North-Holland, 1989, 517--545.

[53] Appendix on set theory. in {\bf Handbook of Boolean algebras.} North--Holland 1989 1213--1233.

[54] Bibliography. in {\bf Handbook of Boolean algebras}. North--Holland 1989, 11269--1342.

[55] Cardinal functions on Boolean algebras.} Birkh\"auser--Verlag, 1990, 152pp.

[56] Structure problems for cylindric algebras.} Colloq. Math. Soc. J. Bolyai 54, 1991, Budapest, Hungary, 413--429.

[57] (editor, with H. Andr\'eka, I. N\'emeti) {\bf Algebraic Logic.} North--Holland, 1991, 746pp.

[58] {\it Remarks on the problems in the books Cylindric Algebras, Part I and Part II and Cylindric Set Algebras.} Colloq. Math. Soc. J. Bolyai 54, 1991, Budapest, Hungary, 723--726.

[59] {\it Corrections for the books Cylindric Algebras, Part I and Part II and Cylindric Set Algebras.} Colloq. Math. Soc. J. Bolyai 54, 1991, Budapest, Hungary, 719--722.

[60] (with S. Koppelberg) Pseudo-trees and Boolean algebras. Order 8, 1992 359--374.

[61] Lectures on cylindric set algebras. Banach Center Publications 28, 1993, 253--290.

[62] Problems in the set theory of Boolean algebras. Mathematica Japonica 42, 1995, 179--185.

[63] Cardinal Invariants on Boolean algebras. Birkh\"auser--Verlag, 1996, 298pp.

[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 [61].)

[71] Boolean algebras. Entry in Stanford Encyclopedia of Philosophy (electronic) (2002).

[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.", (2014) Birkhauser, 59-66.

[86] A large list of small cardinal characteristics of Boolean algebras. Math. Logic Quarterly

Abstracts:

[1] Nonrepresentable polyadic algebras of finite degree. Notices of the AMS, 7 (1960), 735.

[2] Polyadic Heyting algebras. Notices of the AMS, 7 (1960), 735.

[3] Representation theorems for cylindricc algebras. Notices of the AMS, 7 (1960), 1000.

[4] Relation algebras and cylindric algebras. Notices of the AMS, 8 (1961), 358.

[5] On finite dimensional cylindric algebras. Notices of the AMS, 9 (1962), 470.

[6] (with F. M. Sioson) m-semigroups, semigroups, and function representations. Notices of the AMS, 12 (1965), 549-550.

[7] Nonfinitizability of classes of cylindric algebras. Notices of the AMS, 15 (1968), 353.

[8] On the lattice of equational classes of one- and two-dimensional polyadic algebras. Notices of the AMS, 16 (1969), 183.

[9] (with P. Sparks) Counting Boolean algebras. Notices of the AMS, 18 (1971), 551

[10] Independent subsets of subsets of free Boolean algebras. Notices of the AMS 25 (1978), A-3.

[11] (With R. McKenzie) Chains in Boolean algebras. Abstracts of papers presented to the AMS 2(985), 235.

[12] Remarks on Boolean algebras: complete embeddings, independence, tightness Abstracts of papers presented to the AMS 2 (1981), 236.

[13] (with H. Andreka, I. Nemeti) Homomorphic images of weak cylindric algebras with infinite bases. Abstracts of papers presented to the AMS 5 (1984), 470.

[14] (with A. Dow) Compact scattered spaces, tightness, depth, and pi- character. Abstracts of papers presented to the AMS 15 (1994), 558.

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; also, solutions for exercises

(6) Lectures on model theory

(7) Lectures on logic (completeness and incompleteness)

(8) The Banach-Tarski paradox

(9) Non-standard analysis

(10) Undergraduate set theory

(11) Notions of real numbers in set theory

(12) Notes on set theory