A class of -preduals which are isomorphic to quotients of
For every countable ordinal α, we construct an -predual which is isometric to a subspace of and isomorphic to a quotient of . However, is not isomorphic to a subspace of .
A class of sets whose distance set fills an interval
A classification of ordinals up to Borel isomorphism
We consider the Borel structures on ordinals generated by their order topologies and provide a complete classification of all ordinals up to Borel isomorphism in ZFC. We also consider the same classification problem in the context of AD and give a partial answer for ordinals ≤ω₂.
A continuum of totally incomparable hereditarily indecomposable Banach spaces
A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
A generalized version of the singular cardinals problem
A Note On Ultrapower Cardinality
A note on ultrapower cardinality.
A problem on series of ordinals
A Remark On Filter Regularity
A remark on filter regularity.
A well ordering of the Cartesian product of two ordinals
Accumulation functions on the ordinals
Algebraic equivalence of ordinal numbers
Algorithmic representations of Wermus' constructions of ordinal numbers
An ordering of the set of natural numbers based on Peano axioms
Arithmetic of cuts and cuts of classes
Borel extensions of Baire measures in ZFC
We prove: 1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel extension. 2) If the continuum is not real-valued-measurable then every Baire measure on M. E. Rudin's Dowker space admits a Borel extension. Consequently, Balogh's space remains the only candidate to be a ZFC counterexample to the measure extension problem of the three presently known ZFC Dowker spaces.
Built-up systems of fundamental sequences and hierarchies of number-theoretic functions.
Cardinal and ordinal arithmetics of -ary relational systems and -ary ordered sets
The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for -ary relational systems. -ary ordered sets are defined as special -ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of or 3. The class of -ary ordered sets is then closed under the cardinal and ordinal operations.
Cardinal arithmetic of general relational systems