Cohesive Powers of Computable Structures

Valentina Harizanov, George Washington University

Cohesive powers of computable structures are effective analogs of ultrapowers, where the role of an ultrafilter is played by a cohesive set of natural numbers. A set is cohesive if it is infinite and cannot be split into two infinite pieces by any computably enumerable set. The inspiration for cohesive powers goes back to Skolem’s 1934 construction of a countable nonstandard model of arithmetic. The elements of a cohesive power are equivalence classes of partial computable functions, so the power is at most countable structure. We will show how cohesive powers could give us nonstandard models with interesting properties.

MC 5501