Aronszajn orderings.
Around cofin
We show the consistency of "there is a nice σ-ideal ℐ on the reals with add(ℐ) = ℵ₁ which cannot be represented as the union of a strictly increasing sequence of length ω₁ of σ-subideals". This answers [Borodulin-Nadzieja and Głąb, Math. Logic Quart. 57 (2011), 582-590, Problem 6.2(ii)].
Around Podewski's conjecture
A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of...
Around splitting and reaping
We prove several results on some cardinal invariants of the continuum which are closely related to either the splitting number or its dual, the reaping number .
Around stable forking
We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.
Assertion Q distinguishes topologically ω* and when regular and
Assignment problem with fuzzy estimates of effectiveness
Associative -dimensional copulas
The associativity of -dimensional copulas in the sense of Post is studied. These copulas are shown to be just -ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.
Asymmetric tie-points and almost clopen subsets of
A tie-point of compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. We review some of the many consistency results that have depended on the construction of tie-points of . One especially important application, due to Veličković, was to the existence of nontrivial involutions on . A tie-point of has been called symmetric if it is the unique fixed point of an involution. We define the notion of an almost clopen set...
Asymptotic density, computable traceability, and 1-randomness
Let r ∈ [0,1]. A set A ⊆ ω is said to be coarsely computable at density r if there is a computable function f such that {n | f(n) = A(n)} has lower density at least r. Our main results are that A is coarsely computable at density 1/2 if A is computably traceable or truth-table reducible to a 1-random set. In the other direction, we show that if a degree a is hyperimmune or PA, then there is an a-computable set which is not coarsely computable at any positive density.
Asymptotical behaviour of some non-uniform measures
Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces
Asymptotique dans un corps de Hardy
Atomic compactness and elementary equivalence
Atomic compactness for reflexive graphs
A first order structure with universe M is atomic compact if every system of atomic formulas with parameters in M is satisfiable in provided each of its finite subsystems is. We consider atomic compactness for the class of reflexive (symmetric) graphs. In particular, we investigate the extent to which “sparse” graphs (i.e. graphs with “few” vertices of “high” degree) are compact with respect to systems of atomic formulas with “few” unknowns, on the one hand, and are pure restrictions of their...
Atomic compactness in - categorical Horn theories
Atomicity of lattice effect algebras and their sub-lattice effect algebras
We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions...
Autohomeomorphism groups of spaces with unique non-isolated point
Automata, Borel functions and real numbers in Pisot base
This note is about functions ƒ : Aω → Bω whose graph is recognized by a Büchi finite automaton on the product alphabet A x B. These functions are Baire class 2 in the Baire hierarchy of Borel functions and it is decidable whether such function are continuous or not. In 1920 W. Sierpinski showed that a function is Baire class 1 if and only if both the overgraph and the undergraph of f are Fσ. We show that such characterization is also true for functions on infinite words if we replace the real...
Automata-based representations for infinite graphs
New compact representations of infinite graphs are investigated. Finite automata are used to represent labelled hyper-graphs which can be also multi-graphs. Our approach consists of a general framework where vertices are represented by a regular prefix-free language and edges are represented by a regular language and a function over tuples. We consider three different functions over tuples: given a tuple the first function returns its first difference, the second one returns its suffix and the last...