Ramified analysis and the minimal β-models of higher order arithmetics
Random orderings and unique ergodicity of automorphism groups
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...
Rational points on algebraic varieties over a generalized real closed field: a model theoretic approach.
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...
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.
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 prime models for Boolean algebras
Reduced powers of -trees
Reduced products of infinite forcing systems.
Reduced Products Of Saturated Intuitionistic Theories
Reduced products of saturated intuitionistic theories.
Reducing hyperarithmetic sequences
Refined Morley numbers
Regular elements and Green's relations in Menger algebras of terms
Defining an (n+1)-ary superposition operation on the set of all n-ary terms of type τ, one obtains an algebra of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation there are different possibilities to define binary associative operations on the set and on the cartesian power . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative operations...
Regular languages definable by Lindström quantifiers
In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.
Regular languages definable by Lindström quantifiers
In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.
Relation entre le rang U et le poids
Relational quotients
Let 𝒦 be a class of finite relational structures. We define ℰ𝒦 to be the class of finite relational structures A such that A/E ∈ 𝒦, where E is an equivalence relation defined on the structure A. Adding arbitrary linear orderings to structures from ℰ𝒦, we get the class 𝒪ℰ𝒦. If we add linear orderings to structures from ℰ𝒦 such that each E-equivalence class is an interval then we get the class 𝒞ℰ[𝒦*]. We provide a list of Fraïssé classes among ℰ𝒦, 𝒪ℰ𝒦 and 𝒞ℰ[𝒦*]. In addition, we classify...
Relations between Shy Sets and Sets of -Measure Zero in Solovay’s Model
An example of a non-zero non-atomic translation-invariant Borel measure on the Banach space is constructed in Solovay’s model. It is established that, for 1 ≤ p < ∞, the condition "-almost every element of has a property P" implies that “almost every” element of (in the sense of [4]) has the property P. It is also shown that the converse is not valid.