Champs de Markov cachés flous et segmentation d'images
Changing cofinality of a measurable cardinal (An alternative proof)
Changing cofinality of cardinals
Changing measurable into accessible cardinals [Book]
Characteristic of Rings. Prime Fields
The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.
Characteristic sets of a system of equivalence relations
Characterization of a full set of probabilities on some posets.
Characterization of binary operations on the unit interval satisfying the generalized modus ponens inference rule.
Characterization of generic extensions of models of set theory
Characterizations of certain classes of posets having Gs-lattices of a relatively small size
Characterizations of certain general and reproductive solutions of arbitrary equations
Characterizations of commuting relations
Characterizing the polynomial hierarchy by alternating auxiliary pushdown automata
Characterizing the powerset by a complete (Scott) sentence
This paper is part II of a study on cardinals that are characterizable by a Scott sentence, continuing previous work of the author. A cardinal κ is characterized by a Scott sentence if has a model of size κ, but no model of size κ⁺. The main question in this paper is the following: Are the characterizable cardinals closed under the powerset operation? We prove that if is characterized by a Scott sentence, then is (homogeneously) characterized by a Scott sentence, for all 0 < β₁ < ω₁....
Characterizing tolerance trivial finite algebras
An algebra is tolerance trivial if where is the lattice of all tolerances on . If contains a Mal’cev function compatible with each , then is tolerance trivial. We investigate finite algebras satisfying also the converse statement.
Charakter von Mengensystemen.
Charakterisierung der Aufzählungsreduzierbarkeit.
Choice functions and well-orderings over the infinite binary tree
We give a new proof showing that it is not possible to define in monadic second-order logic (MSO) a choice function on the infinite binary tree. This result was first obtained by Gurevich and Shelah using set theoretical arguments. Our proof is much simpler and only uses basic tools from automata theory. We show how the result can be used to prove the inherent ambiguity of languages of infinite trees. In a second part we strengthen the result of the non-existence of an MSO-definable well-founded...
Choice Mappings of Certain Classes of Finite Sets.
Choice principles in elementary topology and analysis
Many fundamental mathematical results fail in ZF, i.e., in Zermelo-Fraenkel set theory without the Axiom of Choice. This article surveys results — old and new — that specify how much “choice” is needed precisely to validate each of certain basic analytical and topological results.