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Tapani Hyttinen

Publications and source records attributed to Tapani Hyttinen.

43 records · Page 3Linked to original sources
arXiv2001

Potential isomorphism and semi-proper trees

We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the cardinality of the models. We introduce the notions of semi-proper and weakly semi-proper trees, and note that there is a strong connection between the existence of potentially isomorphic models for a given complete theory and the existence of weakly semi-proper trees. We prove the existence of semi-proper trees under certain cardinal arithmetic assumptions. We also show the consistency of the non-existence of weakly semi-proper trees assuming the consistency of some large cardinals.

math.LO↗
arXiv2001

Forcing a Boolean Algebra with predesigned automorphism group

For suitable groups G we will show that one can add a Boolean algebra B by forcing in such a way that Aut(B) is almost isomorphic to G. In particular, we will give a positive answer to the following question due to J.Roitman: Is aleph_{omega} a possible number of automorphisms of a rich Boolean algebra?

math.LO↗
arXiv1999

Strong splitting in stable homogeneous models

We study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in [T. Hyttinen, On nonstructure of elementary submodels of a stable homogeneous structure, Fundamenta Mathematicae, 156(1998): 167-182]. We apply this to prove a structure theorem. We also show that dop and sdop are essentially equivalent, where the negation of dop is the property we use in our structure theorem and sdop implies nonstructure.

math.LO↗