A cardinal preserving immune partition of the ordinals
A classification of definable forcings on ω1
Under the assumption of the existence of sharps for reals all simply definable posets on are classified up to forcing equivalence.
A large cardinal in the constructible universe
A new construction of a Kurepa tree with no Aronszajn subtree
A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem
We present a proof of the Boolean Prime Ideal Theorem in a transitive model of ZF in which the Axiom of Choice does not hold. We omit the argument based on the full Halpern-Läuchli partition theorem and instead we reduce the proof to its elementary case.
A topological application of flat morasses
We define combinatorial structures which we refer to as flat morasses, and use them to construct a Lindelöf space with points of cardinality , consistent with GCH. The construction reveals, it is hoped, that flat morasses are a tool worth adding to the kit of any user of set theory.
Abelian group extensions and the axiom of constructibility.
Borel equivalence and isomorphism of coanalytic sets [Book]
Cardinals and iterations of HOD
Cofinalities of complete Boolean algebras.
Compact covering mappings and cofinal families of compact subsets of a Borel set
Among other results we prove that the topological statement “Any compact covering mapping between two Π⁰₃ spaces is inductively perfect” is equivalent to the set-theoretical statement ""; and that the statement “Any compact covering mapping between two coanalytic spaces is inductively perfect” is equivalent to “Analytic Determinacy”. We also prove that these statements are connected to some regularity properties of coanalytic cofinal sets in (X), the hyperspace of all compact subsets of a Borel...
Consistency of the Silver dichotomy in generalised Baire space
Silver’s fundamental dichotomy in the classical theory of Borel reducibility states that any Borel (or even co-analytic) equivalence relation with uncountably many classes has a perfect set of classes. The natural generalisation of this to the generalised Baire space for a regular uncountable κ fails in Gödel’s L, even for κ-Borel equivalence relations. We show here that Silver’s dichotomy for κ-Borel equivalence relations in for uncountable regular κ is however consistent (with GCH), assuming...
Constructibility and shiftings of view
Constructibility in Ackermann's set theory [Book]
Cotorsion-free algebras as endomorphism algebras in - the discrete and topological cases
The discrete algebras over a commutative ring which can be realized as the full endomorphism algebra of a torsion-free -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...
Countably metacompact spaces in the constructible universe
We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a . In addition some nonperfect spaces with σ-disjoint bases are constructed.
Definable Ramsey and definable Erdös ordinals.
Degrees of non-definability of the Sacks model
Deux relations dénombrables, logiquement équivalentes pour le second ordre, sont isomorphes
Die Struktur kartesischer Produkte ganzer Zahlen modulo kartesische Produkte ganzer Zahlen.