Rational points on algebraic varieties over a generalized real closed field: a model theoretic approach.
R.E. degrees of continuous functionals.
Real and imaginary classes in the alternative set theory
Real classes in the ultrapower of hereditarily finite sets
Real closed exponential fields
Ressayre considered real closed exponential fields and “exponential” integer parts, i.e., integer parts that respect the exponential function. In 1993, he outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre’s construction and then analyze the complexity. Ressayre’s construction is canonical once we fix the real closed exponential field R, a residue field section k, and a well ordering ≺ on R. The...
Realisierung und Auswahlaxiom
Reasoning in Basic Description Logics and Description Logics with Modal Operators
Recent developments in the theory of Borel reducibility
Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible to a countable...
Recent developments in the theory of partitions.
Recognizable filters and ideals
Recognizing the topology of the space of closed convex subsets of a Banach space
Reconstructibility of Boolean control networks with time delays in states
This paper deals with the reconstructibility of Boolean control networks (BCNs) with time delays in states. First, a survey on the semi-tensor product, weighted pair graph, constructed forest and finite automata is given. Second, by using the weighted pair graph, constructed forest and finite automata, an algorithm is designed to judge whether a Boolean control network with time delays in states is reconstructable or not under a mild assumption. Third, an algorithm is proposed to determine the current...
Rectangular axioms, perfect set properties and decomposition
Rectangular square-bracket operation for successor of regular cardinals
We give a uniform proof that holds for every regular cardinal λ.
Rectilinearization of functions definable by a Weierstrass system and its applications
This paper presents several theorems on the rectilinearization of functions definable by a convergent Weierstrass system, as well as their applications to decomposition into special cubes and quantifier elimination.
Recursion in total functionals of finite type
Recursion theoretic operators and morphisms on numbered sets
Recursive Arithmetic of Skolem II.
Recursive expansions
Let A be a recursive structure, and let ψ be a recursive infinitary sentence involving a new relation symbol. The main result of the paper gives syntactical conditions which are necessary and sufficient for every recursive copy of A to have a recursive expansion to a model of ψ, provided A satisfies certain decidability conditions. The decidability conditions involve a notion of rank. The main result is applied to prove some earlier results of Metakides-Nerode and Goncharov. In these applications,...
Recursive inseparability of the sets of identically valid and finitely refutable formulas of some elementary theories of varieties.