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Approximations of lattice-valued possibilistic measures

Ivan Kramosil (2005)

Kybernetika

Lattice-valued possibilistic measures, conceived and developed in more detail by G. De Cooman in 1997 [2], enabled to apply the main ideas on which the real-valued possibilistic measures are founded also to the situations often occurring in the real world around, when the degrees of possibility, ascribed to various events charged by uncertainty, are comparable only quantitatively by the relations like “greater than” or “not smaller than”, including the particular cases when such degrees are not...

Archimedean atomic lattice effect algebras in which all sharp elements are central

Zdena Riečanová (2006)

Kybernetika

We prove that every Archimedean atomic lattice effect algebra the center of which coincides with the set of all sharp elements is isomorphic to a subdirect product of horizontal sums of finite chains, and conversely. We show that every such effect algebra can be densely embedded into a complete effect algebra (its MacNeille completion) and that there exists an order continuous state on it.

Archimedean frames, revisited

Jorge Martinez (2008)

Commentationes Mathematicae Universitatis Carolinae

This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called joinfitness and is Choice-free. Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an infinitesimal element arises naturally,...

Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz Tsaban, Lyubomyr Zdomskyy (2016)

Fundamenta Mathematicae

We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property α 1 . 5 is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space C p ( X ) of continuous real-valued functions on X with the topology...

Arithmetical transfinite induction and hierarchies of functions

Z. Ratajczyk (1992)

Fundamenta Mathematicae

We generalize to the case of arithmetical transfinite induction the following three theorems for PA: the Wainer Theorem, the Paris-Harrington Theorem, and a version of the Solovay-Ketonen Theorem. We give uniform proofs using combinatorial constructions.

Arithmetization of the field of reals with exponentiation extended abstract

Sedki Boughattas, Jean-Pierre Ressayre (2008)

RAIRO - Theoretical Informatics and Applications


 (1) Shepherdson proved that a discrete unitary commutative semi-ring A+ satisfies IE0 (induction scheme restricted to quantifier free formulas) iff A is integral part of a real closed field; and Berarducci asked about extensions of this criterion when exponentiation is added to the language of rings. Let T range over axiom systems for ordered fields with exponentiation; for three values of T we provide a theory ⌞ T ⌟ in the language of rings plus exponentiation such that the ...

Around cofin

Andrzej Rosłanowski, Saharon Shelah (2014)

Colloquium Mathematicae

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

Krzysztof Krupiński, Predrag Tanović, Frank O. Wagner (2013)

Fundamenta Mathematicae

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...

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