Department of Foundations of Mathematics
Head:
Staff:
 Marek Cuth (Assistant Professor)
email
pok.509, tel.: 22 5228 178
 Michal Doucha (Assistant Professor)
email
pok. 420, tel.: 22 5228 167
 Ryszard Frankiewicz (Professor)
email
Division in Wrocław
 Piotr Koszmider (Professor)
email
pok. 505, tel.: 22 5228 148
 Marcin Sabok (Assistant Professor)
email
pok.420, tel.: 22 5228 167
 Hector Gabriel Salazar Pedroza (Assistant Professor)
email
pok.613, tel.: 22 5228 213
Phd Students:
About the Department
Research of the Section involves a rather wide spectrum of matters which
are
connected with the foundations of mathematics, such as set theory, elements of
functional analysis, elements of real analysis, foundations of arithmetic, cathegorical logic.
Zofia Adamowicz
Zofia Adamowicz is working in foundations of arithmetic.
Her main research
is in
"bounded arithmetic" together with its links to computational complexity and the P=NP
problem. Recent research concerns the power of the exponential function in
arithmetic, e.g. its influence on the existence of end extensions of models.
Some recent papers:

A contribution to the endextension problem and the Π_{1}
conservativeness problem, Ann. Pure Appl. Logic 61, pp. 348, 1993.
 Existentially Closed Structures and Gödel's Second Incompleteness Theorem (with T. Bigorajska), J. Symb. Log, 66(1), pp. 349356, 2001.

On Herbrand consistency in weak arithmetic (with P. Zbierski),
Arch. Math. Logic, 40(6), pp. 399413, 2001
 Herbrand Consistency and Bounded Arithmetic, Fundamenta Mathematica, 171, pp. 279292, 2002

On complexity reduction of Σ_{1} formulas (with P.
Zbierski), Arch.
Math. Logic 42(1), pp. 4558, 2003.
 Wellbehaved principles alternative to bounded induction (with L. A. Kołodziejczyk), Theor. Comput. Sci. 322(1), pp. 516, 2004.
 Partial collapses of the Sigma_{1} complexity hierarchy in models for fragments of bounded arithmetic (with L. A. Kołodziejczyk and P. Zbierski), Ann. Pure Appl. Logic, 145(1), pp. 9195, 2007.
 Lower bounds for the unprovability of Herbrand consistency in weak arithmetics (with K. Zdanowski), submitted.
Also she is a coauthor of a handbook of logic:
 Logic of Mathematics (with P. Zbierski),
Wiley, 1997.
Ryszard Frankiewicz
His research interest includes: infinite combinatorics,
applications of set theory to mathematical analysis, in particular: the
algebra P(ω)/fin, the groups of automorphisms of Boolean
algebras, unconditional bases in Banach spaces, discontinuous
homomorphisms of Banach algebras.
Some recent publications:

Hausdorff Gaps and Limits,
Stud. Logic Found. Math. 132, NorthHolland, 1994
(with P. Zbierski).

Borel liftings of the measure algebra and
the failure of the continuum hypothesis, Proc.
Amer. Math. Soc. 120 (1994), 12471250 (with T. Carlson and P. Zbierski).

Nonaccessible filters in measure algebras and
functionals on L_{∞}(Λ)^{*}, Studia Math. 108
(1994), 191200 (with G. Plebanek).

On asymptotic density and uniformly distributed
sequences, Studia Math. 119 (1996), 1726 (with
G. Plebanek).

Convex combinations and weak^{*} null
sequences, Bull. Polish Acad. Sci. 45
(1997), 221225 (with G. Plebanek).

On closed Psets without ccc in the space ω^{*},
Israel J. Math. (with S. Shelah
and P. Zbierski), to appear.

Fat Psets in the space ω^{*},
J. Symbolic Logic (with P. Zbierski), to appear.
Piotr Koszmider
His research is focused on developing and applications of the methods of
combinatorial set theory and logic such as forcing, stepping up,
antiRamsey results, bookkeeping principles in analysis and topology in
particular in Banach spaces, weak and weak* topology and in algebras of
operators.
Some recent publications:

A. Aviles, P. Koszmider, A continuous image of a RadonNikodym compact
space which is not RadonNikodym; To appear in Duke Math. J.
 A. Avilés, P. Koszmider; A Banach space in which every injective
operator is surjective. To apepar in Bull. London Math. Soc.
 Piotr Koszmider; On large indecomposable Banach spaces; J. Funct. Anal.
264 (2013), no. 8, 1779805
 Jesus Ferrer, Piotr Koszmider, Wieslaw Kubis; Almost disjoint families
of countable sets and separable complementation properties; J. Math.
Anal. Appl. 401 (2013), no. 2, 939949
 Christina Brech, Piotr Koszmider; On universal spaces for the class of
Banach spaces whose dual balls are uniform Eberlein compacts; Proc.
Amer. Math. Soc. 141 (2013), 12671280
 Piotr Koszmider; A C(K) Banach space which does not have the
SchroederBernstein property; Studia Math. 212 (2012), 95117
 Christina Brech, Piotr Koszmider; On universal Banach spaces of density
continuum, Israel J. Math. 190 (2012), 93110
Czesław RyllNardzewski
His research
interests include mathematical logic, set theory, descriptive
set theory, topology, probability theory and stochastic processes,
functional and harmonic analysis, real analysis,
ergodic theory, differential equations.
He is an author (or coauthor) of many
well known and important results, including,
to mention but a few: RyllNardzewski theorem on categoricity,
the theorem on impossibility of finite axiomatization of
arithmetic,
RyllNardzewski
fixed point theorem,
Kuratowski and RyllNardzewski
selector theorem.
Konrad Zdanowski
His research interests includes arithmetics with bounded induction,
finite model theory, intuitionistic logic, philosophy of mathematics.
Publications:

On Spectra of formulae with Henkin Quantifiers
(with J. Golińska), in Philosophical Dimensions of Logic and
Science, Proc.of LMPhSc 1999, ed. A. Rojszczak, J. Cachro, G.
Kurczewski, Kluwer, 2003, pp. 2945.
 Degrees of logics with Henkin Quantifiers (with M. Mostowski), in Archive for Mathematical Logic, 43(2004), pp.691702.
 Theories of arithmetics in finite models (with M. Krynicki), in Journal of Symbolic Logic, 70(2005), pp. 128.
 FMrepresentability and beyond (with M. Mostowski), Proc. of CiE 2005, Lecture Notes in Computer Science vol. 3526, Springer, pp.358367.
 Coprimality in finite models
(with M. Mostowski), Proc. of CSL 2005, Lecture Notes in Computer
Science, vol. 3634, Springer, pp.
263275.
 Finite Arithmetics (with M. Krynicki and M. Mostowski), Fundamenta Informaticae, vol. 81(2007), pp. 183202.
 The Intended Model of Arithmetic. An Argument from Tennenbaum's Theorem
(with P. Quinon), in Computation and Logic in the Real World, CiE
2007, Local Proceedings, ed. S.B. Cooper, B. Loewe i A. Sorbi,
2007.
 Undecidability and concatenation
(with A. Grzegorczyk), in Andrzej Mostowski and Foundational Studies,
ed. W. Marek, A. Ehrenfeucht, M. Srebrny, IOS Press, Amsterdam, 2008.
 On the second order intuitionistic propositional logic without a universal quantifier, submitted.
 Lower bounds for the unprovability of Herbrand consistency in weak arithmetics (with Z. Adamowicz), submitted.
 On a question of Andreas Weiermann (with H. Kotlarski), submitted.