Curriculum Vita vita.tex Latex 2e vita.ps Postscript vita.pdf PDF Acrobat	Some interesting problems problems.abs Abstract in plain ascii problems.tex Latex 2e problems.ps Postscript problems.pdf PDF Acrobat

Mathscinet Link to mrauthid=124855
Preprint archive arxiv.org au:Miller_Arnold_W ... Arxiv has first versions.
What are these file extensions?

Borel Hierarchies - lecture notes from a course (m873-14)
I gave Spring 2014. Still under construction Fall 2017.
bor.tex .. bor.pdf

Lecture: On the length of Borel hierarchies
July 2016
Kurt Godel Research Center, Vienna, Austria and
TOPOSYM, Prague, Czech Republic.
slides len.tex .. len.pdf
lecture notes length.tex .. length.pdf

Nyikos's Joke
eprint March 2016
ny.abs .. ny.tex .. ny.pdf ..

The onto mapping property of Sierpinski
eprint July 2014 updated May 2016
abstract .. sier.tex .. sier.pdf

Analytic subspace of the reals without an analytic basis
(with Konstantinos Beros)
eprint June 2014 (written Feb 2009)
analbase.tex .. analbase.pdf

Partitions of 2^omega and Completely Ultrametrizable Spaces
(with William R. Brian)
Topology Appl. 184 (2015), 61-71.
abstract .. ucr.tex .. ucr.pdf

A proof by areas of the sin(A+B) formula.
I came up with this, but it wouldn't surprise me if it was already
known hundreds of years ago.

Selective covering properties of product spaces, II: gamma spaces
(with Boaz Tsaban, Lyubomyr Zdomskyy)
Trans. Amer. Math. Soc. 368 (2016), no. 4, 2865-2889.
arxiv ..

Irredundant Generators
(with Jonathan Cancino, Osvaldo Guzm\'an)
eprint June 2013 revised Apr 2014
irr.tex .. irr.pdf
Retitled: Ideal independent families and the ultrafilter number,
Journal of Symbolic Logic, 86(2021), 128-136.

Generating Borel measurable mappings with continuous mappings
(with Wojciech Bielas, Micha{\l} Morayne, Tomasz S{\l}onka)
Topology Appl. 160 (2013), no. 12, 1439-1443.
bmms.pdf

Countable subgroups of Euclidean Space
eprint May 2013
abstract .. ctblgrps.tex .. ctblgrps.ps .. ctblgrps.pdf .. ctblgrps.dvi ..

Selective covering properties of product spaces
(with Boaz Tsaban, Lyubomyr Zdomskyy)
Annals of Pure and Applied Logic 165 (2014), 1034-1057.
arxiv ..

Compact subsets of the Baire space
eprint Nov 2012
abstract .. mic.tex .. mic.ps .. mic.pdf .. mic.dvi ..

A hierarchy of clopen graphs on the Baire space
eprint Oct 2012
abstract .. clopen.tex .. clopen.ps .. clopen.pdf .. clopen.dvi ..

Carlson collapse is minimal under MA
eprint Sept 2012
carlson.tex .. carlson.pdf

Cohen forcing preserves being a gamma-set
but not Hurewicz property
eprint Sept 2012
cohen.tex .. cohen.pdf

Products of Luzin, Sierpinski, and gamma-sets
These three results answer questions raised by Boaz Tsaban.
Tsaban and Zdomskyy have greatly generalized them as well as
proving many other results on the covering properties of products.
eprints July 2012
luzin.tex .. luzin.pdf
luzin2.tex .. luzin2.pdf
prod.tex .. prod.pdf

Recurse - question of Charlie McCoy
eprint July 2012
recurse.tex .. recurse.ps .. recurse.pdf .. recurse.dvi ..

Hechler and Laver Trees
eprint Apr 2012
hechler.abs .. hechler.tex .. hechler.ps .. hechler.pdf .. hechler.dvi ..
hechler-remarks.txt ..

Universal Functions
(with P.Larson, J.Steprans, W.Weiss)
Fund. Math. 227 (2014), no. 3, 197--246.
univ.abs .. univ.tex .. univ.ps .. univ.pdf .. univ.dvi ..

Absoluteness of convexly orderable
eprint Feb 2012
convex.tex .. convex.ps .. convex.pdf .. convex.dvi ..

The hierarchy of $\omega_1$-Borel sets
eprint July 2011
omega1.abs .. omega1.tex .. omega1.ps .. omega1.pdf .. omega1.dvi ..

Uniquely Universal Sets
Topology and its Applications 159 (2012), pp. 3033-3041.
hrus.abs .. hrus.tex .. hrus.ps .. hrus.pdf .. hrus.dvi ..

The maximum principle in forcing and the axiom of choice
eprint May 2011
max.abs .. max.tex .. max.ps .. max.pdf .. max.dvi ..

Universal sets for pointsets properly on the n^^th level of the
projective hierarchy
to appear Journal of Symbolic Logic
(with Greg Hjorth and Leigh Humphries)
hhm.abs .. hhm.tex .. hhm.ps .. hhm.pdf .. hhm.dvi ..

Point-cofinite covers in the Laver model
Proceedings of American Mathematical Society, 138(2010), 3313-3321.
(with B. Tsaban)
unb.abs .. unb.tex .. unb.ps .. unb.pdf .. unb.dvi ..

Kunen biography ... kunen-bio.pdf

The axiom of choice and two-point sets in the plane
eprint Sept 2008
two-pt.abs .. two-pt.tex .. two-pt.ps .. two-pt.pdf .. two-pt.dvi ..

Lecture notes on interest rate calculations for business students
eprint Dec 2008
int.pdf

A Dedekind Finite Borel Set
Arch. Math. Logic 50 (2011), no. 1-2, 1--17.
ded.abs .. ded.tex .. ded.ps .. ded.pdf .. ded.dvi ..
Proof of Remark 3.4 .. remark.tex .. remark.pdf

The Recursion Theorem and Infinite Sequences
eprint Nov 2007
recur.abs .. recur.tex .. recur.ps .. recur.pdf .. recur.dvi ..

Lecture notes in Computability Theory
137 pages
eprint Dec 2008
m773-07

Long Borel hierarchies
Math Logic Quarterly, 54(2008), 301-316.
longbor.abs .. longbor.tex .. longbor.ps .. longbor.pdf .. longbor.pdf ..
remarks

A hodgepodge of sets of reals
Note di Matematica, 27(2007), Supplemento 1, 25-39.
podge.abs .. podge.tex .. podge.ps .. podge.pdf .. podge.dvi ..

Steinhaus Sets and Jackson sets
Advances in logic, 127--145, Contemp. Math., 425, Amer. Math. Soc., 2007.
(with S.Gao, W. Weiss)
jack.abs .. jack.tex .. jack.ps .. jack.pdf .. jack.dvi ..

The number of translates of a closed nowhere dense set
required to cover a Polish group
Annals of Pure and Applied Logic, 140(2006), 52-59
(with Juris Steprans)
cnd.abs .. cnd.tex .. cnd.ps .. cnd.pdf .. cnd.dvi ..

Half of an inseparable pair
Real Analysis Exchange, 32 (2006/07), no. 1, 179--193.
insep.abs .. insep.tex .. insep.ps .. insep.pdf .. insep.dvi ..

Cardinal characteristic for relative $\gamma$ -sets
Topology and its Applications, 156(2009), 872-878.
relgamma.abs .. relgamma.tex .. relgamma.ps .. relgamma.pdf .. relgamma.dvi ..

On squares of spaces and $F_\sigma$-sets
Topology Proceedings, 20(2005), 237-241.
square.abs .. square.tex .. square.ps .. square.pdf .. square.dvi ..

The $\gamma$ -Borel conjecture
Archive for Mathematical Logic, 44(2005), 425-434.
gammabc.abs .. gammabc.tex .. gammabc.ps .. gammabc.pdf .. gammabc.dvi ..

Models in which every nonmeager set is nonmeager in a
nowhere dense Cantor set
Canadian Journal of Mathematics, 57(2005), 1139-1154.
(with M.Burke)
nonmeag.abs .. nonmeag.tex .. nonmeag.ps .. nonmeag.pdf .. nonmeag.dvi ..

Ultrafilters with property (s)
Proceedings of the American Mathematical Society, 137(2009), 3115-3121
ultra-s.abs .. ultra-s.tex .. ultra-s.ps .. ultra-s.pdf .. ultra-s.dvi ..

On $\lambda'$-sets
Topology Proceedings, 28(2004), 179-187.
lambda.abs ... lambda.tex ... lambda.ps ... lambda.pdf ... lambda.dvi ...

On relatively analytic and Borel subsets
Journal of Symbolic Logic 70(2005), 346-352.
rel-anal.abs .. rel-anal.tex .. rel-anal.ps .. rel-anal.pdf .. rel-anal.dvi ..

Descriptive set theory ...
in Encyclopedia of general topology. Edited by Klaas Pieter
Hart, Jun-iti Nagata and Jerry E. Vaughan. Elsevier Science
Publishers, B.V., Amsterdam, 2004. x+526 pp. ISBN: 0-444-50355-2
encyc.pdf

A MAD Q-set
Fundamenta Mathematicae, 178(2003), 271-281.
madq.abs ... madq.tex ... madq.ps ... madq.pdf ... madq.dvi ...

A nonhereditary Borel-cover $\gamma$ set
Real Analysis Exchange, 29(2003-2004), 601-606.
borgamma.abs ... borgamma.tex ... borgamma.ps ... borgamma.pdf ... borgamma.dvi ...

Categoricity Without Equality
in {\L}os Memorial Volume, Fundamenta Mathematicae, 170(2001), 87-106.
(with H. Jerome Keisler)
equal.abs ... equal.tex ... equal.ps ... equal.pdf

Baire measures on uncountable product spaces
eprint Oct 1998
baire.abs ... baire.tex ... baire.ps ... baire.pdf

Vitali sets and Hamel bases that are
Marczewski measurable
Fundamenta Mathematicae, 166(2000), 269-279.
(with Strashimir G. Popvassilev)
hamel.abs ... hamel.tex ... hamel.ps ... hamel.pdf ...

Everywhere of Second Category Sets
Real Analysis Exchange, 24(1999), 607-614.
(with K.Muthuvel)
every.abs ... every.tex ... every.ps ... every.pdf

Orthogonal Families of Real Sequences
Journal of Symbolic Logic, 63(1998), 29-49.
(with J.Steprans)
orthog.abs ... orthog.tex ... orthog.ps ... orthog.pdf

Introduction to Mathematical Logic - Moore style
This is a set of 288 questions written for a Moore-style course
in Mathematical Logic, 75 pages.
eprint 1996
logintro.abs ... logintro.tex ... logintro.ps ... logintro.pdf ...

Mathematical Logic and Computability
McGraw-Hill (1996)
(with J. Keisler, K. Kunen, T. Millar, J. Robbin)
book.pdf

The combinatorics of open covers (II)
Topology and its applications, 73(1996), 241-266.
(with W.Just, M.Scheepers, and P.J. Szeptycki)
jmss.abs ... jmss.tex ... jmss.ps ... jmss.pdf ...

Souslin's Hypothesis and Convergence in Category
Proceedings of American Mathematical Society, 124(1996), 1529-1532.
converge.abs ... converge.tex ... converge.ps ... converge.pdf ...

Cardinal invariants concerning functions
whose sum is almost continuous
Real Analysis Exchange, 20(1994-5), 657-672.
(with K.Ciesielski)
almost.abs ... almost.tex ... almost.ps ... almost.pdf ...

Measurability of functions with approximately continuous
vertical sections and measurable horizontal sections
Colloquium Mathematicae, 69(1995), 299-308.
(with M.Laczkovich)
approx.abs ... approx.tex ... approx.ps ... approx.pdf ...

Descriptive Set Theory and Forcing:
how to prove theorems about Borel sets the hard way
Lecture Notes in Logic 4(1995), Springer-Verlag.
New edition 4-2001 now published by Association for Symbolic Logic.
dstfor.abs ... dstfor.tex ... dstfor.ps ... dstfor.pdf

Measurable rectangles
Real Analysis Exchange, 19(1994), 194-202.
rectang.abs ... rectang.tex ... rectang.ps ... rectang.pdf

Some interesting problems
in Set Theory of the Reals, ed Haim Judah, Israel Mathematical
Conference Proceedings, 6(1993), 645-654, American Math Society
problems.pdf

Special sets of reals
in Set Theory of the Reals, ed Haim Judah, Israel Mathematical
Conference Proceedings, 6(1993), 415-432, American Math Society.
survey.abs ... survey.tex ... survey.ps ... survey.pdf

Sacks forcing, Laver forcing, and Martin's axiom
Archive for Mathematical Logic, 31(1992), 145-161.
(with H.Judah and S.Shelah)
sacks.abs ... sacks.tex ... sacks.ps ... sacks.pdf .. sacks.dvi ..

Review: Countable Ultraproducts Without CH by Michael Canjar;
Small Filter Forcing by R. Michael Canjar
The Journal of Symbolic Logic Vol. 56, No. 1, Mar., 1991
jstor

Projective subsets of separable metric spaces
Annals of Pure and Applied Logic, 50(1990), 53-69.
proj.abs ... proj.tex ... proj.ps ... proj.pdf ...

Set theoretic properties of Loeb measure
Journal of Symbolic Logic, 55(1990), 1022-1036.
loeb.abs ... loeb.tex ... loeb.ps ... loeb.pdf ...

Solution to a problem of Hagendorf (with K.Kunen)
Letter to Fraisse July 1987
hagen.tex .. hagen.ps .. hagen.pdf .. hagen.dvi ..

Review: R. Fraisse, Theory of relations
Bulletin of the American Mathematical Society
Volume 23, Number 1 July 1990
project euclid

Two remarks about analytic sets
in Lecture Notes in Mathematics, Springer-Verlag, 1401(1989), 68-72.
(with F.van Engelen and K.Kunen)
tworem.abs ... tworem.tex ... tworem.ps ... tworem.pdf ...

Descriptive Set Theory Over Hyperfinite Sets
Journal of Symbolic Logic, 54(1989), 1167-1180.
(with H. Jerome Keisler, Kenneth Kunen, Steven Leth)
abstract ... hyper.ps ... hyper.pdf

Infinite combinatorics and definability
Annals of Pure and Applied Mathematical Logic, 41(1989), 179-203.
infcomb.abs ... infcomb.tex ... infcomb.ps ... infcomb.pdf ...

Review: Can You Take Solovay's Inaccessible Away? by Saharon Shelah;
A Mathematical Proof of S. Shelah's Theorem on the Measure
Problem and Related Results by Jean Raisonnier
The Journal of Symbolic Logic Vol. 54, No. 2, Jun., 1989
jstor

Rigid Borel sets and better quasiorder theory
Contemporary Mathematics (American Mathematical Society), 65(1987), 199-222.
(with Fons van Engelen and John Steel)
rigid.pdf

On some properties of Hurewicz, Menger, and Rothberger
Fundamenta Mathematicae, 129(1988), 17-33.
(with David H. Fremlin)
abstract ... hmr.pdf

fun-solution.pdf Solution to Funar problem in 1986 Math Monthly
fun-guy.pdf Letter from Guy.
fun-letter.pdf Letter from Funar.
fun-problem.pdf Math Monthly problem statement see p.280
fun-maa.pdf Math Monthly Guy column see p.966 first paragraph.

Rational perfect set forcing
Contemporary Mathematics (American Mathematical Society), 31(1984), 143-159.
rat.pdf

When the continuum has cofinality $\omega_1$
Pacific Journal of Mathematics, 115(1984), 399-407.
(with Karel Prikry)
cofone.pdf

Additivity of Measure Implies Dominating Reals
Proceedings of the American Mathematical Society, 91(1984), 111-117.
abstract ... addmeas.ps ... addmeas.pdf

(with Larry Manevitz) Lindeloff models of the reals: solution to a problem of Sikorski
Israel Journal of Mathematics, 45(1983), 209-218.
lind.pdf

Borel and projective sets from the point of view of compact sets
Mathematical Proceedings of the Cambridge Philosophical Society, 94(1983), 399-409.
(with Ken Kunen)
pov.pdf

A Minimal Degree Which Collapses $\omega_1$
Journal of Symbolic Logic, 49(1984), 298-300.
(with Tim Carlson, Kenneth Kunen)
abstract ... min.pdf

$\gamma$ -sets and other singular sets of real numbers
Topology and Its Applications, 17(1984), 145-155.
(with Fred Galvin)
abstract ... gamma.pdf

Special subsets of the real line
in Handbook of Set Theoretic Topology, North Holland, (1984), 201-233.
special.pdf

Review: The Number of Countable Models by Michael Morley
The Journal of Symbolic Logic Vol. 49, No. 1, Mar., 1984
jstor

The Borel classification of the isomorphism class of a countable model
Notre Dame Journal of Formal Logic, 24(1983), 22-34.
ctblemod.pdf

Pellings problem
American Mathematical Monthly, Vol. 90, No. 6, Jun. - Jul., 1983, 408-9.
pelling.pdf

On box products
Topology and Its Applications, 14(1982), 313-317.
abstract ... box.pdf

A Characterization of the Least Cardinal for which the Baire Category Theorem Fails
Proceedings of the American Mathematical Society, 86(1982), 498-502.
abstract ... char.ps ... char.pdf

Review: On the Consistency of Borel's Conjecture by Richard Laver;
Iterated Perfect-Set Forcing by James E. Baumgartner; Richard Laver
The Journal of Symbolic Logic Vol. 48, No. 3, Sep., 1983
jstor

Mapping a Set of Reals Onto the Reals
Journal of Symbolic Logic, 48(1983), 575-584.
abstract ... map.ps ... map.pdf

Generic Souslin sets
Pacific Journal of Mathematics, 97(1981), 171-181.
gensous.pdf

Some Properties of Measure and Category
Transactions of the American Mathematical Society, 266(1981), 93-114.
abstract ... some.ps ... some.pdf ...
Corrections and Additions to "Some Properties of Measure and Category"
Transactions of the American Mathematical Society, 271(1982), 347-348.
abstract ... somecorr.ps ... somecorr.pdf

The Baire Category Theorem and Cardinals of Countable Cofinality
Journal of Symbolic Logic, 47(1982), 275-288.
abstract ... ctble.ps ... ctble.pdf

On generating the category algebra and the Baire order problem
Bulletin de L'Academie Polonaise des Science, 27(1979), 751-755.
gen.pdf ...

Covering $2^\omega$ with $\omega_1$ disjoint closed sets
in The Kleene Symposium, North Holland (1980), 415-421.
cov.pdf ...

On Q Sets
Proceedings of the American Mathematical Society, 78(1980), 280-284.
(with William G. Fleissner)
abstract ... qsets.ps ... qsets.pdf

Vaught's conjecture for theories of one unary operation
Fundamenta Mathematicae, 111(1981), 135-141.
abstract ... vc.pdf

There are no Q-Points in Laver's Model for the Borel Conjecture
Proceedings of the American Mathematical Society, 78(1980), 103-106.
abstract ... laver.pdf

On the length of Borel hierarchies
Annals of Math Logic, 16(1979), 233-267.
hier.pdf

Some problems in set theory and model theory
Thesis (Ph.D. in Mathematics)--University of California, Berkeley, Nov. 1978.
thesis.pdf