in 2005, a. abdollahi and a. rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. in thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. we have extend the previous knownresults to semigroups and groups satisfying this concept.

In 2005, A. Abdollahi and A. Rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. In thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. We have extend the previous knownresults to semigroups and groups satisfying this concept.

We show that every locally finite bipartite Borel graph satisfying a strengthening of Hall’s condition has a Borel perfect matching on some comeager invariant Borel set. We apply this to show that if a group acting by Borel automorphisms on a Polish space has a paradoxical decomposition, then it admits a paradoxical decomposition using pieces having the Baire property. This strengthens a theore...

2) Suppose that Γ is a 4-paradoxical group and Γ = A1∪A2∪B1∪B2 is a paradoxical decomposition as defined above. Show that Γ plays ping-pong on itself, where the pingpong players are a := a−1 1 a2 and b := b −1 1 b2 .Deduce that Γ contains a non-abelian free subgroup F2. 3) Define the Tarski number T (Γ) of a group Γ to be the smallest integer N if it exists such that Γ is N -paradoxical. By the...

Call a set A ⊆ R paradoxical if there are disjoint A0, A1 ⊆ A such that both A0 and A1 are equidecomposable with A via countabbly many translations. X ⊆ R is hereditarily nonparadoxical if no uncountable subset of X is paradoxical. Penconek raised the question if every hereditarily nonparadoxical set X ⊆ R is the union of countably many sets, each omitting nontrivial solutions of x − y = z − t....

In this paper we extend the approach of M. Cavaleri to effective amenability class computably enumerable groups, i.e. in particular do not assume that groups are finitely generated. case computable also study complexity set all F{\o}lner sequences and paradoxical decomposition. appendix attach a version "On decidability groups" by K. Duda A. Ivanov which covers Sections 9 10 from previous versi...

sometimes disagreement in regards to reading a qur’ānic verse has resulted in a paradoxical judgment and this occurs in traditions, as well. but the way in which one can consider paradoxical verses arises from the so-called ‘alājīyah traditions. the question that arises here is as follows: can the rules presented by these evidences be also extended to the paradoxical readings? if so, what are t...

in this research, it has been tried to determine and introduce the relationship between the mystical experience and paradoxical expression. in the first section the major function of these two categories in language has been considered. in the other section some significant questions have been scientifically answered. these questions are: is the paradoxical expression the internal characteristi...