Department of Foundations of Mathematics



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:

Also she is a co-author of a handbook of logic:

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:

Piotr Koszmider

His research is focused on developing and applications of the methods of combinatorial set theory and logic such as forcing, stepping up, anti-Ramsey results, bookkeeping principles in analysis and topology in particular in Banach spaces, weak and weak* topology and in algebras of operators.

Some recent publications:

Czesław Ryll-Nardzewski

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 co-author) of many well known and important results, including, to mention but a few: Ryll-Nardzewski theorem on categoricity, the theorem on impossibility of finite axiomatization of arithmetic, Ryll-Nardzewski fixed point theorem, Kuratowski and Ryll-Nardzewski selector theorem.

Konrad Zdanowski

His research interests includes arithmetics with bounded induction, finite model theory, intuitionistic logic, philosophy of mathematics.