Weakly projectable and projectable W-algebras.
In this paper we introduce and study the weakly projectable and projectable W-algebras and we review the Representation Theorem of [1].
Weierstrass division theorem in definable germs in a polynomially bounded o-minimal structure
We give some examples of polynomially bounded o-minimal expansions of the ordered field of real numbers where the Weierstrass division theorem does not hold in the ring of germs, at the origin of ℝⁿ, of definable functions.
Weighted sums of aggregation operators.
The aim of this work is to investigate when a weighted sum, or in other words, a linear combination, of two or more aggregation operators leads to a new aggregation operator. For weights belonging to the real unit interval, we obtain a convex combination and the answer is known to be always positive. However, we will show that also other weights can be used, depending upon the aggregation operators involved. A first set of suitable weights is obtained by a general method based on the variation of...
Weights of denumerable topological spaces
Well-definable types over subsets
Well-quasi-ordering Aronszajn lines
We show that, assuming PFA, the class of all Aronszajn lines is well-quasi-ordered by embeddability.
What Is A Mathematical Theory?
What machines can and cannot do.
In this paper, the questions of what machines cannot do and what they can do will be treated by examining the ideas and results of eminent mathematicians. Regarding the question of what machines cannot do, we will rely on the results obtained by the mathematicians Alan Turing and Kurt G¨odel. Turing machines, their purpose of defining an exact definition of computation and the relevance of Church-Turing thesis in the theory of computability will be treated in detail. The undecidability of the “Entscheidungsproblem”...
What the finitization problem is not
What was an irrational number to an ancient Greek mathematician?
When a first order T has limit models
We sort out to a large extent when a (first order complete theory) T has a superlimit model in a cardinal λ. Also we deal with related notions of being limit.
When a partial Borel order is linearizable
When does the Katětov order imply that one ideal extends the other?
We consider the Katětov order between ideals of subsets of natural numbers ("") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).
When is an equivalance relation classifiable.
When is Lindelöf?
Theorem. In ZF (i.e., Zermelo-Fraenkel set theory without the axiom of choice) the following conditions are equivalent: (1) is a Lindelöf space, (2) is a Lindelöf space, (3) is a Lindelöf space, (4) every topological space with a countable base is a Lindelöf space, (5) every subspace of is separable, (6) in , a point is in the closure of a set iff there exists a sequence in that converges to , (7) a function is continuous at a point iff is sequentially continuous at , (8)...
When is the orbit algebra of a group an integral domain ? Proof of a conjecture of P.J. Cameron
Cameron introduced the orbit algebra of a permutation group and conjectured that this algebra is an integral domain if and only if the group has no finite orbit. We prove that this conjecture holds and in fact that the age algebra of a relational structure R is an integral domain if and only if R is age-inexhaustible. We deduce these results from a combinatorial lemma asserting that if a product of two non-zero elements of a set algebra is zero then there is a finite common tranversal of their...
When is the union of an increasing family of null sets?
We study the problem in the title and show that it is equivalent to the fact that every set of reals is an increasing union of measurable sets. We also show the relationship of it with Sierpi'nski sets.
Whitehead Modules over Domains.
Whitehead property of modules
Why semisets?