Every nuclear Fréchet space with a regular basis has the quasi-equivalence property

Every Countable Group Has the Weak Rohlin Property

We present a simple proof of the fact that every countable group Γ is weak Rohlin, that is, there is in the Polish space AΓ of measure preserving Γ-actions an action T whose orbit in AΓ under conjugations is dense. In conjunction with earlier results this in turn yields a new characterization of non-Kazhdan groups as those groups which admit such an action T which is also ergodic.

The Quasi-morphic Property of Group

A group is called morphic if for each normal endomorphism α in end(G),there exists β such that ker(α)= Gβ and Gα= ker(β). In this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= Gβ and Gα = ker(γ). We call G quasi-morphic, if this happens for any normal endomorphism α in end(G). We get the following results: G is quasi-morphic if and only if, for any ...

Every Body Has a Brain

[1] http://ebhb.morphonix.com/ [2] http://fireflyfoundation.wordpress.com/brain-games/every-body-has-a-brain/ [3] http://dev.cdgr.ucsb.edu/organizations/morphonix [4] http://dev.cdgr.ucsb.edu/category/genre/educational [5] http://dev.cdgr.ucsb.edu/category/genre/music/dance [6] http://dev.cdgr.ucsb.edu/category/topics/anatomy [7] http://dev.cdgr.ucsb.edu/category/topics/brain [8] http://dev.cdg...

Every Algorithm Has a POV

Unary negation fragment with equivalence relations has the finite model property

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property. More specifically, we show that every satisfiable formula has a model of at most doubly exponential size. We argue that the satisfiability (= finite satisfiabil...