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Papers by Andrzej Roslanowski

Math. Slovaca, 2018

We are interested in subgroups of the reals that are small in one and large in another sense. We ... more We are interested in subgroups of the reals that are small in one and large in another sense. We prove that, in ZFC, there exists a non–meager Lebesgue null subgroup of R, while it is consistent that there there is no non–null meager subgroup of R. This answers a question from Filipczak, Ross lanowski and Shelah [4].

Topology and its Applications, 2000

Fundamenta Mathematicae, Mar 14, 1997

We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of... more We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate some new cardinal invariants.

Journal of Applied Analysis, 1997

Notre Dame Journal of Formal Logic, Apr 20, 2011

. We introduce stronger properties of ultrafilters and we show that those properties may be handl... more . We introduce stronger properties of ultrafilters and we show that those properties may be handled in lambda-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal lambda with generating system of size less than 2^lambda . We also show how reasonable ultrafilters can be killed by forcing notions which have enough reasonable completeness to be iterated with lambda-supports (and we show the appropriate preservation theorem).

Arch Math Log, 1996

We prove that the Sacks forcing collapses the continuum onto the dominating number d, answering t... more We prove that the Sacks forcing collapses the continuum onto the dominating number d, answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses omega_2 then it forces diamond_{omega_1} .

Colloquium Mathematicum, 2001

Jsyml, 1998

Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Bore... more Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F subseteq P(X) of size c, consisting of Borel sets which are not in I. Condition (M) states that there is a function f:X-> X with f^{-1}[{x}] notin I for each x in X. Provided that X is a group and I is invariant, condition (D) states that there exist a Borel set B notin I and a perfect set P subseteq X for which the family {B+x: x in P} is disjoint. The aim of the paper is to study whether the reverse implications in the chain (D) => (M) => (B) => not-ccc can hold. We build a sigma-ideal on the Cantor group witnessing''(M) and not (D)'' (Section 2). A modified version of that sigma-ideal contains the whole space (Section 3). Some consistency results deriving (M) from (B) for''nicely'' defined ideals are established (Section 4). We show that both ccc and (M) can fail (Theorems 1.3 and 4.2). Finally, some sharp versions of (M) for invariant ideals on Polish groups are investigated (Section 5).

Transactions of the American Mathematical Society, 2005

The Journal of Symbolic Logic, 1996

Proceedings of the American Mathematical Society, 1990

Notre Dame Journal of Formal Logic, 2011

International Journal of Mathematics and Mathematical Sciences, 2001

Colloquium Mathematicum, 2001

Colloquium Mathematicum, 2001

Archive for Mathematical Logic, 1996

Math. Slovaca, 2018

We are interested in subgroups of the reals that are small in one and large in another sense. We ... more We are interested in subgroups of the reals that are small in one and large in another sense. We prove that, in ZFC, there exists a non–meager Lebesgue null subgroup of R, while it is consistent that there there is no non–null meager subgroup of R. This answers a question from Filipczak, Ross lanowski and Shelah [4].

Topology and its Applications, 2000

Fundamenta Mathematicae, Mar 14, 1997

We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of... more We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate some new cardinal invariants.

Journal of Applied Analysis, 1997

Notre Dame Journal of Formal Logic, Apr 20, 2011

. We introduce stronger properties of ultrafilters and we show that those properties may be handl... more . We introduce stronger properties of ultrafilters and we show that those properties may be handled in lambda-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal lambda with generating system of size less than 2^lambda . We also show how reasonable ultrafilters can be killed by forcing notions which have enough reasonable completeness to be iterated with lambda-supports (and we show the appropriate preservation theorem).

Arch Math Log, 1996

We prove that the Sacks forcing collapses the continuum onto the dominating number d, answering t... more We prove that the Sacks forcing collapses the continuum onto the dominating number d, answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses omega_2 then it forces diamond_{omega_1} .

Colloquium Mathematicum, 2001

Jsyml, 1998

Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Bore... more Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F subseteq P(X) of size c, consisting of Borel sets which are not in I. Condition (M) states that there is a function f:X-> X with f^{-1}[{x}] notin I for each x in X. Provided that X is a group and I is invariant, condition (D) states that there exist a Borel set B notin I and a perfect set P subseteq X for which the family {B+x: x in P} is disjoint. The aim of the paper is to study whether the reverse implications in the chain (D) => (M) => (B) => not-ccc can hold. We build a sigma-ideal on the Cantor group witnessing''(M) and not (D)'' (Section 2). A modified version of that sigma-ideal contains the whole space (Section 3). Some consistency results deriving (M) from (B) for''nicely'' defined ideals are established (Section 4). We show that both ccc and (M) can fail (Theorems 1.3 and 4.2). Finally, some sharp versions of (M) for invariant ideals on Polish groups are investigated (Section 5).

Transactions of the American Mathematical Society, 2005

The Journal of Symbolic Logic, 1996

Proceedings of the American Mathematical Society, 1990

Notre Dame Journal of Formal Logic, 2011

International Journal of Mathematics and Mathematical Sciences, 2001

Colloquium Mathematicum, 2001

Colloquium Mathematicum, 2001

Archive for Mathematical Logic, 1996

For a cardinal λ < λω 1 we give a ccc forcing notion P such that P " some Σ 0 2 set B ⊆ ω 2 admit... more For a cardinal λ < λω 1 we give a ccc forcing notion P such that P " some Σ 0 2 set B ⊆ ω 2 admits a sequence ηα : α < λ of distinct elements of ω 2 such that (ηα + B) ∩ (η β + B) ≥ 6 for all α, β < λ but does not have a perfect set of such η's ". The construction closely follows the one from Shelah [6, Section 1].

We show that, consistently, there is a Borel set which has un-countably many pairwise very non-di... more We show that, consistently, there is a Borel set which has un-countably many pairwise very non-disjoint translations, but does not allow a perfect set of such translations.