Clones, coclones and coconnected spaces.
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.
Collectionwise Hausdorff property in product spaces
Combinatorics and quantifiers
Let be the set of subsets of of cardinality . Let be a coloring of and a coloring of . We write if every -homogeneous is also -homogeneous. The least such that for some is called the -width of and denoted by . In the first part of the paper we prove the existence of colorings with high -width. In particular, we show that for each and there is a coloring with . In the second part of the paper we give applications of wide colorings in the theory of generalized quantifiers....
Combinatory logic and the ω-rule
Comments on Ultraproducts of Forcing Systems
Compacidad Y Decibilidad De Logicas Monadicas Con Cuantificadores Cardinales.
Compact and ...-compact formulas in L..., ...
Compactness and chromatic number
Compactness and homogeneity of saturated structures. I.
Compactness and homogeneity of saturated structures. II.
Compactness and homomorphisms of algebraic structures
Compactness and Löwenheim-Skolem properties in categories of pre-institutions
The abstract model-theoretic concepts of compactness and Löwenheim-Skolem properties are investigated in the "softer" framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institution. These results rely on notions of compact transformation, which are introduced as arrow-oriented generalizations...
Compactness of Powers of ω
We characterize exactly the compactness properties of the product of κ copies of the space ω with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in elementary extensions. We also have results involving products of possibly uncountable regular cardinals.
Compactness=JEP in any logic
Comparing the succinctness of monadic query languages over finite trees
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog. Succinctness...
Comparing the succinctness of monadic query languages over finite trees
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog. Succinctness...
Compatible Idempotent Terms in Universal Algebra
In universal algebra, we oftentimes encounter varieties that are not especially well-behaved from any point of view, but are such that all their members have a “well-behaved core”, i.e. subalgebras or quotients with satisfactory properties. Of special interest is the case in which this “core” is a retract determined by an idempotent endomorphism that is uniformly term definable (through a unary term ) in every member of the given variety. Here, we try to give a unified account of this phenomenon....
Complete and model-complete theories of monadic algebras
Complete description for -equivalence types of superatomic -algebras.