A simple proof of the hereditary undecidability of the theory of lattice-ordered abelian groups

1985 ◽  
Vol 20 (3) ◽  
pp. 400-401 ◽  
Author(s):  
Stanley Burris
Keyword(s):  
Simple Proof ◽  
Abelian Groups ◽  
Hereditary Undecidability

scholarly journals Actions of finite rank: weak rational ergodicity and partial rigidity

2015 ◽  
Vol 36 (7) ◽  
pp. 2138-2171 ◽  
Author(s):  
ALEXANDRE I. DANILENKO
Keyword(s):  
Simple Proof ◽  
Finite Rank ◽  
Abelian Groups ◽  
Interval Exchange ◽  
Infinite Measure ◽  
Interval Exchange Transformations ◽  
Bratteli Diagrams ◽  
Rank One ◽  
Partial Rigidity ◽  
Definition Of

A simple proof of the fact that each rank-one infinite measure preserving (i.m.p.) transformation is subsequence weakly rationally ergodic is found. Some classes of funny rank-one i.m.p. actions of Abelian groups are shown to be subsequence weakly rationally ergodic. A constructive definition of finite funny rank for actions of arbitrary infinite countable groups is given. It is shown that the ergodic i.m.p. transformations of balanced finite funny rank are subsequence weakly rationally ergodic. It is shown that the ergodic probability preserving transformations of exact finite rank, the ergodic Bratteli–Vershik maps corresponding to the ‘consecutively ordered’ Bratteli diagrams of finite rank, some their generalizations and the ergodic interval exchange transformations are partially rigid.

Undecidable Lt theories of topological abelian groups

1981 ◽  
Vol 46 (4) ◽  
pp. 761-772 ◽  
Author(s):  
Gregory L. Cherlin ◽  
Peter H. Schmitt
Keyword(s):  
Abelian Groups ◽  
Torsion Free ◽  
Hereditary Undecidability

AbstractWe prove the hereditary undecidability of the Lt theories of:(1) torsion-free Hausdorff topological abelian groups;(2) locally pure Hausdorff topological abelian groups.

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

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