Arnold W. Miller

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All published works

Action	Title	Year	Authors
+	IDEAL INDEPENDENT FAMILIES AND THE ULTRAFILTER NUMBER	2021	Jonathan Cancino-Manríquez Osvaldo Guzmán Arnold W. Miller
+	Hereditarily countable sets	2017	Arnold W. Miller
+	Borel order of a field of sets	2017	Arnold W. Miller
+	Generic G<sub>δ</sub>	2017	Arnold W. Miller
+	Proof of Louveau's Theorem	2017	Arnold W. Miller
+	Borel metric spaces and lines in the plane	2017	Arnold W. Miller
+	Covering number of an ideal	2017	Arnold W. Miller
+	Large sets	2017	Arnold W. Miller
+	CH and orders of separable metric spaces	2017	Arnold W. Miller
+	Louveau's Theorem	2017	Arnold W. Miller
+	Abstract Borel hierarchies	2017	Arnold W. Miller
+ PDF Chat	Selective covering properties of product spaces, II: $\gamma $ spaces	2015	Arnold W. Miller Boaz Tsaban Lyubomyr Zdomskyy
+	Partitions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>ω</mml:mi></mml:mrow></mml:msup></mml:math> and completely ultrametrizable spaces	2015	William R. Brian Arnold W. Miller
+	Remark 3.4 A Dedekind Finite Borel Set	2015	Arnold W. Miller
+	The onto mapping property of Sierpinski	2014	Arnold W. Miller
+	Partitions of 2^{\omega} and completely ultrametrizable spaces	2014	William R. Brian Arnold W. Miller
+	Selective covering properties of product spaces	2014	Arnold W. Miller Boaz Tsaban Lyubomyr Zdomskyy
+ PDF Chat	Universal functions	2014	Paul Larson Arnold W. Miller Juris Steprāns William Weiss
+	The onto mapping property of Sierpinski	2014	Arnold W. Miller
+	Partitions of 2^ω and completely ultrametrizable spaces	2014	William R. Brian Arnold W. Miller
+	Generating Borel measurable mappings with continuous mappings	2013	Wojciech Bielas Arnold W. Miller Michał Morayne Tomasz Słonka
+	Universal sets for pointsets properly on the <i>n</i><sup>th</sup> level of the projective hierarchy	2013	Greg Hjorth Leigh Humphries Arnold W. Miller
+	Countable subgroups of Euclidean Space	2013	Arnold W. Miller
+	Uniquely universal sets	2012	Arnold W. Miller
+	Universal Functions	2012	Paul Larson Arnold W. Miller Juris Steprāns William Weiss
+	Hechler and Laver Trees	2012	Arnold W. Miller
+	A hierarchy of clopen graphs on the Baire space	2012	Arnold W. Miller
+	Universal Functions	2012	Paul Larson Arnold W. Miller Juris Steprāns William Weiss
+	The maximum principle in forcing and the axiom of choice	2011	Arnold W. Miller
+	The hierarchy of omega1-Borel sets	2011	Arnold W. Miller
+	Uniquely Universal Sets	2011	Arnold W. Miller
+	The maximum principle in forcing and the axiom of choice	2011	Arnold W. Miller
+ PDF Chat	Point-cofinite covers in the Laver model	2010	Arnold W. Miller Boaz Tsaban
+ PDF Chat	A dedekind finite borel set	2010	Arnold W. Miller
+ PDF Chat	Ultrafilters with property $( {s})$	2009	Arnold W. Miller
+	The hierarchy of !1-Borel sets	2009	Arnold W. Miller
+	The cardinal characteristic for relative γ-sets	2008	Arnold W. Miller
+	Long Borel hierarchies	2008	Arnold W. Miller
+	The Recursion Theorem and Infinite Sequences	2008	Arnold W. Miller
+	Lecture notes on set theory without choice	2008	Arnold W. Miller
+	A Dedekind Finite Borel Set	2008	Arnold W. Miller
+	A hodgepodge of sets of reals	2007	Arnold W. Miller
+ PDF Chat	Steinhaus sets and Jackson sets	2007	Su Gao Arnold W. Miller William Weiss
+	Half of an Inseparable Pair	2007	Arnold W. Miller
+	Long Borel Hierarchies	2007	Arnold W. Miller
+	A hodgepodge of sets of reals	2006	Arnold W. Miller
+	Steinhaus Sets and Jackson Sets	2006	Su Gao Arnold W. Miller William Weiss
+	A hodgepodge of sets of reals	2006	Arnold W. Miller
+ PDF Chat	Models in Which Every Nonmeager Set is Nonmeager in a Nowhere Dense Cantor Set	2005	Maxim R. Burke Arnold W. Miller
+ PDF Chat	The number of translates of a closed nowhere dense set required to cover a Polish group	2005	Arnold W. Miller Juris Steprāns
+ PDF Chat	On relatively analytic and Borel subsets	2005	Arnold W. Miller
+	The γ-borel conjecture	2004	Arnold W. Miller
+	Half of an inseparable pair	2004	Arnold W. Miller
+	On squares of spaces and Fsigma-sets	2004	Arnold W. Miller
+ PDF Chat	A Nonhereditary Borel-cover γ-set	2004	Arnold W. Miller
+	The cardinal characteristic for relative gamma-sets	2004	Arnold W. Miller
+	The number of translates of a closed nowhere dense set required to cover a Polish group	2004	Arnold W. Miller Juris Steprāns
+	Half of an inseparable pair	2004	Arnold W. Miller
+ PDF Chat	A MAD Q-set	2003	Arnold W. Miller
+	Descriptive Set Theory	2003	Arnold W. Miller
+	Ultrafilters with property (s)	2003	Arnold W. Miller
+	On relatively analytic and Borel subsets	2003	Arnold W. Miller
+	Models in which every nonmeager set is nonmeager in a nowhere dense Cantor set	2003	Maxim R. Burke Arnold W. Miller
+	A nonhereditary Borel-cover gamma-set	2003	Arnold W. Miller
+	The gamma - Borel conjecture	2003	Arnold W. Miller
+	On lambda'-sets	2002	Arnold W. Miller
+	A Mad Q-set	2002	Arnold W. Miller
+	On lambda'-sets	2002	Arnold W. Miller
+	A Mad Q-set	2002	Arnold W. Miller
+ PDF Chat	Categoricity without equality	2001	H. Jerome Keisler Arnold W. Miller
+	Vitali sets and Hamel bases that are Marczewski measurable	2000	Arnold W. Miller Strashimir G. Popvassilev
+ PDF Chat	Vitali sets and Hamel bases that are Marczewski measurable	2000	Arnold W. Miller Strashimir G. Popvassilev
+ PDF Chat	Orthogonal families of real sequences	1998	Arnold W. Miller Juris Steprāns
+ PDF Chat	The combinatorics of open covers II	1996	Winfried Just Arnold W. Miller Marion Scheepers Paul J. Szeptycki
+	Some interesting problems	1996	Arnold W. Miller
+ PDF Chat	Souslin’s hypothesis and convergence in category	1996	Arnold W. Miller
+	Introduction to mathematical logic - A problem solving course	1996	Arnold W. Miller
+ PDF Chat	Measurability of functions with approximately continuous vertical sections and measurable horizontal sections	1996	Miklós Laczkovich Arnold W. Miller
+	Some interesting problems	1996	Arnold W. Miller
+	The combinatorics of open covers (II)	1995	Winfried Just Arnold W. Miller Marion Scheepers Paul J. Szeptycki
+	Orthogonal Families of Real Sequences	1995	Arnold W. Miller Juris Steprāns
+	Chapter 10: CH and orders of separable metric spaces	1995	Arnold W. Miller
+	Chapter 31: Borel metric spaces and lines in the plane	1995	Arnold W. Miller
+	Chapter 19: Hereditarily countable sets	1995	Arnold W. Miller
+	Chapter 25: Large $\Pi^1_2$ sets	1995	Arnold W. Miller
+	Chapter 34: Proof of Louveau's Theorem	1995	Arnold W. Miller
+	Chapter 9: Borel order of a field of sets	1995	Arnold W. Miller
+	Borel order of a field of sets	1995	Arnold W. Miller
+	Louveau’s Theorem	1995	Arnold W. Miller
+	CH and orders of separable metric spaces	1995	Arnold W. Miller
+	Proof of Louveau’s Theorem	1995	Arnold W. Miller
+	Covering number of an ideal	1995	Arnold W. Miller
+	Borel metric spaces and lines in the plane	1995	Arnold W. Miller
+	Abstract Borel hierarchies	1995	Arnold W. Miller
+	Large % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa % aeqabaWaaeaaeaaakeaacqGHpis1daqhaaWcbaGaeGOmaidabaGaeG % ymaedaaaaa!3310! $$ \prod _2^1 $$ sets	1995	Arnold W. Miller
+	% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa % aeqabaWaaeaaeaaakeaanabaaaaaaaaapeGaeyyeIu+aa0baa4qaai % abikdaYaqaaiabigdaXaaaaaa!3352! $$ \sum _2^1 $$ well-orderings	1995	Arnold W. Miller
+	Descriptive Set Theory and Forcing	1995	Arnold W. Miller
+	Hereditarily countable sets	1995	Arnold W. Miller
+	% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa % aeqabaWaaeaaeaaakeaacqGHpis1daqhaaWcbaGaeGymaedabaGaeG % ymaedaaaaa!330E! $$ \prod _1^1 $$ equivalence relations	1995	Arnold W. Miller
+	% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa % aeqabaWaaeaaeaaakeaacqGHris5daqhaaWcbaGaeGymaedabaGaeG % ymaedaaaaa!3320! $$ \sum _1^1 $$ equivalence relations	1995	Arnold W. Miller
+	Orthogonal Families of Real Sequences	1995	Arnold W. Miller Juris Steprāns
+	The combinatorics of open covers (II)	1995	Winfried Just Arnold W. Miller Marion Scheepers Paul J. Szeptycki
+	Cardinal invariants concerning functions whose sum is almost continuous	1994	Krzysztof Ciesielski Arnold W. Miller
+	Descriptive set theory and forcing; How to prove theorems about Borel sets the hard way	1994	Arnold W. Miller
+	Measurability of functions with approximately continuous vertical sections and measurable horizontal sections	1994	Miklós Laczkovich Arnold W. Miller
+	Souslin's Hypothesis and Convergence in Category	1994	Arnold W. Miller
+	Cardinal invariants concerning functions whose sum is almost continuous	1994	Krzysztof Ciesielski Arnold W. Miller
+ PDF Chat	Sacks forcing, Laver forcing, and Martin's axiom	1992	Haim Judah Arnold W. Miller Saharon Shelah
+	Measurable rectangles	1992	Arnold W. Miller
+	Projective subsets of separable metric spaces	1990	Arnold W. Miller
+	Set theoretic properties of Loeb measure	1990	Arnold W. Miller
+ PDF Chat	Book Review: Theory of relations	1990	Arnold W. Miller
+	Descriptive set theory over hyperfinite sets	1989	H. Jerome Keisler Kenneth Kunen Arnold W. Miller Steven Leth
+	Descriptive set theory over hyperfinite sets	1989	H. Jerome Keisler Kenneth Kunen Arnold W. Miller Steven Leth
+	Shelah Saharon, Can you take Solovay's inaccessible away? Israel journal of mathematics, vol. 48 (1984), pp. 1–47.Raisonnier Jean, A mathematical proof of S. Shelah's theorem on the measure problem and related results, Israel journal of mathematics, vol. 48 (1984), pp. 48–56.	1989	Arnold W. Miller
+	Infinite combinatorics and definability	1989	Arnold W. Miller
+	Two remarks about analytic sets	1989	Fons van Engelen Kenneth Kunen Arnold W. Miller
+ PDF Chat	On some properties of Hurewicz, Menger, and Rothberger	1988	Arnold W. Miller David Fremlin
+ PDF Chat	When the continuum has cofinalityω1	1984	Arnold W. Miller Karel Prikry
+ PDF Chat	Additivity of Measure Implies Dominating Reals	1984	Arnold W. Miller
+ PDF Chat	A minimal degree which collapses ω<sub>1</sub>	1984	Tim Carlson Kenneth Kunen Arnold W. Miller
+	γ-sets and other singular sets of real numbers	1984	Fred Galvin Arnold W. Miller
+ PDF Chat	Additivity of measure implies dominating reals	1984	Arnold W. Miller
+	Special Subsets of the Real Line	1984	Arnold W. Miller
+	Rational perfect set forcing	1984	Arnold W. Miller
+	Borel and projective sets from the point of view of compact sets	1983	Kenneth Kunen Arnold W. Miller
+	Review: Richard Laver, On the Consistency of Borel's Conjecture; James E. Baumgartner, Richard Laver, Iterated Perfect-Set Forcing	1983	Arnold W. Miller
+	Mapping a set of reals onto the reals	1983	Arnold W. Miller
+	Richard Laver. On the consistency of Borel's conjecture. Acta mathematica, vol. 137 no. 3–4 (for 1976, pub. 1977), pp. 151–169. - James E. Baumgartner and Richard Laver. Iterated perfect-set forcing. Annals of mathematical logic, vol. 17 (1979), pp. 271–288.	1983	Arnold W. Miller
+	Lindelöf models of the reals: Solution to a problem of Sikorski	1983	Larry M. Manevitz Arnold W. Miller
+ PDF Chat	On the Borel classification of the isomorphism class of a countable model.	1983	Arnold W. Miller
+ PDF Chat	A Characterization of the Least Cardinal for which the Baire Category Theorem Fails	1982	Arnold W. Miller
+	The Baire category theorem and cardinals of countable cofinality	1982	Arnold W. Miller
+	Corrections and Additions to "Some Properties of Measure and Category"	1982	Arnold W. Miller
+ PDF Chat	A characterization of the least cardinal for which the Baire category theorem fails	1982	Arnold W. Miller
+ PDF Chat	Corrections and additions to: “Some properties of measure and category”	1982	Arnold W. Miller
+	On box products	1982	Arnold W. Miller
+ PDF Chat	Some Properties of Measure and Category	1981	Arnold W. Miller
+ PDF Chat	Some properties of measure and category	1981	Arnold W. Miller
+ PDF Chat	Vaught's conjecture for theories of one unary operation	1981	Arnold W. Miller
+ PDF Chat	On 𝑄 sets	1980	William G. Fleissner Arnold W. Miller
+ PDF Chat	There are no 𝑄-points in Laver’s model for the Borel conjecture	1980	Arnold W. Miller
+	Covering 2ω with ω1 Disjoint Closed Sets	1980	Arnold W. Miller
+ PDF Chat	There are no Q-Points in Laver's Model for the Borel Conjecture	1980	Arnold W. Miller

Common Coauthors

Coauthor	Papers Together
Juris Steprāns	8
Kenneth Kunen	5
William Weiss	5
William R. Brian	3
H. Jerome Keisler	3
Paul Larson	3
Boaz Tsaban	3
Paul J. Szeptycki	3
Marion Scheepers	3
Winfried Just	2
Lyubomyr Zdomskyy	2
Strashimir G. Popvassilev	2
Steven Leth	2
Su Gao	2
Miklós Laczkovich	2
Maxim R. Burke	2
Krzysztof Ciesielski	2
Jonathan Cancino-Manríquez	1
Karel Prikry	1
Fred Galvin	1
Winfried Just	1
Wojciech Bielas	1
William G. Fleissner	1
Haim Judah	1
Larry M. Manevitz	1
Fons van Engelen	1
Leigh Humphries	1
David Fremlin	1
Tomasz Słonka	1
Saharon Shelah	1
Tim Carlson	1
Michał Morayne	1
Greg Hjorth	1
Osvaldo Guzmán	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	On the consistency of Borel's conjecture	1976	Richard Laver	19
+	On the length of Borel hierarchies	1979	Arnorld W. Miller	18
+	Iterated perfect-set forcing	1979	James E. Baumgartner Richard Laver	13
+	γ-sets and other singular sets of real numbers	1984	Fred Galvin Arnold W. Miller	13
+	A Model of Set-Theory in Which Every Set of Reals is Lebesgue Measurable	1970	Robert M Solovay	12
+ PDF Chat	Some properties of measure and category	1981	Arnold W. Miller	12
+	Set Theory An Introduction to Independence Proofs	1980	Kenneth Kunen	12
+	Special Subsets of the Real Line	1984	Arnold W. Miller	10
+ PDF Chat	The combinatorics of open covers II	1996	Winfried Just Arnold W. Miller Marion Scheepers Paul J. Szeptycki	9
+	Iterated Cohen Extensions and Souslin's Problem	1971	R. M. Solovay S. Tennenbaum	9
+ PDF Chat	On 𝑄 sets	1980	William G. Fleissner Arnold W. Miller	9
+	Some properties of C(X), II	1983	J. Gerlits	8
+	Borel sets and Ramsey's theorem	1973	Fred Galvin Karel Prikry	6
+	Analytic determinacy and 0<sup>#</sup>	1978	Leo Harrington	6
+	The Baire category theorem and cardinals of countable cofinality	1982	Arnold W. Miller	6
+ PDF Chat	A characterization of the least cardinal for which the Baire category theorem fails	1982	Arnold W. Miller	6
+	Mapping a set of reals onto the reals	1983	Arnold W. Miller	6
+	Sur les familles indenombrables de suites de nombres naturels et les problemes concernant la propriete<b>C</b>	1941	Fritz Rothberger	5
+	Descriptive Set Theory	1980	Yiannis N. Moschovakis	5
+ PDF Chat	The combinatorics of Borel covers	2002	Marion Scheepers Boaz Tsaban	5
+	Happy families	1977	A. R. D. Mathias	5
+ PDF Chat	Some Properties of Measure and Category	1981	Arnold W. Miller	5
+	Projective subsets of separable metric spaces	1990	Arnold W. Miller	5
+	D. H. Fremlin. Consequences of Martin's axiom. Cambridge tracts in mathematics, no. 84. Cambridge University Press, Cambridge etc. 1984, xii + 325 pp.	1988	Jason Weiss	5
+	Martin's Axiom	1977	MaryEllen Rudin	5
+ PDF Chat	On some properties of Hurewicz, Menger, and Rothberger	1988	Arnold W. Miller David Fremlin	5
+	Combinatorial Cardinal Characteristics of the Continuum	2009	Andreas Blass	5
+ PDF Chat	Some additive properties of sets of real numbers	1981	Paul Erdős Kenneth Kunen R. Daniel Mauldin	5
+	Combinatorics of open covers I: Ramsey theory	1996	Marion Scheepers	5
+ PDF Chat	Sets generated by rectangles	1974	R. H. Bing W. W. Bledsoe R. Daniel Mauldin	5
+	Short complete nested sequences in βN⧹N and small maximal almost-disjoint families	1972	Stephen H. Hechler	4
+ PDF Chat	On the existence of P-points in the Stone-Čech compactification of integers	1976	Jussi Ketonen	4
+ PDF Chat	Summen von $ℵ_1$ Mengen	1936	Felix Hausdorff	4
+ PDF Chat	On some problems of Hausdorff and of Sierpiński	1948	Fritz Rothberger	4
+	A new proof that analytic sets are Ramsey	1974	Erik Ellentuck	4
+	Combinatorics of open covers (VIII)	2003	Liljana Babinkostova Ljubiša D. R. Kočinac Marion Scheepers	4
+	Infinite combinatorics and definability	1989	Arnold W. Miller	4
+	Handbook of Set-Theoretic Topology	1984	Stewart Baldwin	4
+ PDF Chat	Universal co-analytic sets	1996	Greg Hjorth	4
+	Every analytic set is Ramsey	1970	Jack Silver	4
+	Borel and projective sets from the point of view of compact sets	1983	Kenneth Kunen Arnold W. Miller	4
+	Counting the number of equivalence classes of Borel and coanalytic equivalence relations	1980	Jack H. Silver	4
+	Some properties of C(X), I	1982	J. Gerlits Zs. Nagy	4
+ PDF Chat	Sur une classe de fonctions de M. Sierpiński et la classe correspondante d'ensembles	1935	Edward Szpilrajn	4
+ PDF Chat	𝑄-sets do not necessarily have strong measure zero	1988	Jaime I. Ihoda Saharon Shelah	3
+ PDF Chat	Eine Äquivalenz zwischen der Kontniuumhypotlhese und der Existenz der Lusinschen und Sierpińskischen Mengen	1938	Fritz Rothberger	3
+ PDF Chat	$Q$-sets, Sierpiński sets, and rapid filters	1991	Haim Judah Saharon Shelah	3
+ PDF Chat	On discrete Borel spaces and projective sets	1969	B. V. Rao	3
+	Sets Having Calibre	1977	J. K. Truss	3
+	A Separation Theorem for ∑ 1 1 Sets	1980	Alain Louveau	3