We investigate various strong notions of rigidity for Souslin trees, separating them under ♦ into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under ♦ that there is a group whose automorphism tower is highly malleable by forcing.

aim and background: multiple sclerosis (ms) is a chronic inflammatory disease of the central nervous system in which primary symptoms emerges in adults between the age 20 and 40 years old. previous findings indicate 15-20 percent of multiple sclerosis (ms) patients are diagnosed with executive function impairments. the purpose of this study is to evaluate planning function as one of executive f...

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We consider the problem of unfolding lattice polygons embedded on the surface of some classes of lattice polyhedra. We show that an unknotted lattice polygon embedded on a lattice orthotube or orthotree can be convexified in O(n) moves and time, and a lattice polygon embedded on a lattice Tower of Hanoi or Manhattan Tower can be convexified in O(n) moves and time.

By definition, an ω-residually free tower is positive-genus if all surfaces used in its construction are of positive genus. We prove that every limit group is virtually a subgroup of a positive-genus ω-residually free tower. By combining this construction with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups.

........................................................................................................................................................43 Introduction...................................................................................................................................................43 Previous Work .....................................................................

By definition, an ω-residually free tower is positive-genus if all surfaces used in its construction are of positive genus. We prove that every limit group is virtually a subgroup of a positive-genus ω-residually free tower. By combining this construction with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups.

We consider the problem of unfolding lattice polygons embedded on the surface of some classes of lattice polyhedra. We show that an unknotted lattice polygon embedded on a lattice orthotube or orthotree can be convexified in O(n) moves and time, and a lattice polygon embedded on a lattice Tower of Hanoi or Manhattan Tower can be convexified in O(n) moves and time.