Operazioni di Brouwer e realizzabilità formalizzata
Optimal bounds for ordinal comparison maps.
Optimal matrices of partitions and an application to Souslin trees
The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some useful properties, the n-optimal matrices of partitions. We use this to improve a decomposition result for strongly homogeneous Souslin trees. The latter is in turn applied to separate strong notions of rigidity of Souslin trees, thereby answering a considerable portion of a question of Fuchs and Hamkins.
Orbits of denumerable models of complete theories
Order properties of splitting subspaces in an inner product space
Order with successors is not interprétable in RCF
Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.
Ordered fields and the ultrafilter theorem
We prove that on the basis of ZF the ultrafilter theorem and the theorem of Artin-Schreier are equivalent. The latter says that every formally real field admits a total order.
Ordered prime spectra of bounded -monoids
Ordered prime spectra of Boolean products of bounded -monoids are described by means of their decompositions to the prime spectra of the components.
Ordered Rings and Fields
We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].
Ordered ultraconnected rings
Ordering D-classes and computing Schein rank is hard.
Ordering of observables and characterization of conditional expectation
Orderings of Fuzzy Sets Based on Fuzzy Orderings. Part I: The Basic Approach.
Orderings of Fuzzy Sets Based on Fuzzy Orderings Part II: Generalizations.
Order-types of models of arithmetic and a connection with arithmetic saturation.
Ordinal analysis of bar recursion of type zero
Ordinal indices in Banach spaces.
Ordinal remainders of classical ψ-spaces
Let ω denote the set of natural numbers. We prove: for every mod-finite ascending chain of infinite subsets of ω, there exists , an infinite maximal almost disjoint family (MADF) of infinite subsets of the natural numbers, such that the Stone-Čech remainder βψ∖ψ of the associated ψ-space, ψ = ψ(ω,ℳ ), is homeomorphic to λ + 1 with the order topology. We also prove that for every λ < ⁺, where is the tower number, there exists a mod-finite ascending chain , hence a ψ-space with Stone-Čech remainder...
Ordinal ultrafilters versus P-hierarchy
An earlier paper [Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214] investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. The present paper focuses on the aspects of characterization of classes of ultrafilters of finite index, existence, generic existence and the Rudin-Keisler-order.
Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension
We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy problems for ordinary differential equations which have a unique solution is -complete and that the set of Cauchy problems which locally have a unique solution is -complete. We prove that the set of Cauchy problems which have a global solution is -complete...