Classical hierarchies from a modern standpoint. Part II. R-sets
Classification and extension by the transfinite induction
Classification of the regular De Morgan algebras of fuzzy sets.
A characterization of regular lattices of fuzzy sets and their isomorphisms is given in Part I. A characterization of involutions on regular lattices of fuzzy sets and the isomorphisms of De Morgan algebras of fuzzy sets is given in Part II. Finally all classes of De Morgan algebras of fuzzy sets with respect to isomorphisms are completely described.
Classifying Projective-like Hierarchies
Classifying stationary sets: a survey
Clones on regular cardinals
We investigate the structure of the lattice of clones on an infinite set X. We first observe that ultrafilters naturally induce clones; this yields a simple proof of Rosenberg’s theorem: there are maximal (= “precomplete”) clones on a set of size λ. The clones we construct do not contain all unary functions. We then investigate clones that do contain all unary functions. Using a strong negative partition theorem from pcf theory we show that for cardinals λ (in particular, for all successors of...
Clopen graphs
A graph G on a topological space X as its set of vertices is clopen if the edge relation of G is a clopen subset of X² without the diagonal. We study clopen graphs on Polish spaces in terms of their finite induced subgraphs and obtain information about their cochromatic numbers. In this context we investigate modular profinite graphs, a class of graphs obtained from finite graphs by taking inverse limits. This continues the investigation of continuous colorings on Polish spaces and their homogeneity...
Closed discrete subsets of separable spaces and relative versions of normality, countable paracompactness and property
In this paper we show that a separable space cannot include closed discrete subsets which have the cardinality of the continuum and satisfy relative versions of any of the following topological properties: normality, countable paracompactness and property . It follows that it is consistent that closed discrete subsets of a separable space which are also relatively normal (relatively countably paracompact, relatively ) in are necessarily countable. There are, however, consistent examples of...
Club-guessing and non-structure of trees
We study the possibilities of constructing, in ZFC without any additional assumptions, strongly equivalent non-isomorphic trees of regular power. For example, we show that there are non-isomorphic trees of power ω₂ and of height ω · ω such that for all α < ω₁· ω · ω, E has a winning strategy in the Ehrenfeucht-Fraïssé game of length α. The main tool is the notion of a club-guessing sequence.
Club-guessing, good points and diamond
Shelah’s club-guessing and good points are used to show that the two-cardinal diamond principle holds for various values of and .
Cluster sets of arbitrary functions defined on plane sets
Coalgebras for binary methods : properties of bisimulations and invariants
Coalgebras for endofunctors can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard...
Coalgebras for Binary Methods: Properties of Bisimulations and Invariants
Coalgebras for endofunctors can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors. This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many...
Coalitional fuzzy preferences
The paper deals with the concept of coalitional preferences in the group decision-making situations in which the agents and coalitions have only vague idea about the comparative acceptability of particular outcomes. The coalitional games with vague utilities (see, e. g., [6]) can serve for a good example when some types of the game solutions (e. g., the von Neumann– Morgenstern one) are to be extended to the fuzzy game case. In this paper, we consider the fuzzy analogies of coalitional preferences...
Coding that preserves Ramseyness
Cofinal families in certain function spaces
Cofinal types of topological directed orders
We investigate the structure of the Tukey ordering among directed orders arising naturally in topology and measure theory.
Cofinalities of complete Boolean algebras.
Cognitive (Semantic) Visualization of the Continuum Problem and Mirror Symmetric Proofs in the Transfinite Numbers Theory
Cohen real and disjoint refinement of perfect sets
We prove that if there exists a Cohen real over a model, then the family of perfect sets coded in the model has a disjoint refinement by perfect sets.