1,338 research outputs found
Reverse mathematics and infinite traceable graphs
This paper falls within the general program of investigating the proof
theoretic strength (in terms of reverse mathematics) of combinatorial
principals which follow from versions of Ramsey's theorem. We examine two
statements in graph theory and one statement in lattice theory proved by
Galvin, Rival and Sands \cite{GRS:82} using Ramsey's theorem for 4-tuples. Our
main results are that the statements concerning graph theory are equivalent to
Ramsey's theorem for 4-tuples over \RCA while the statement concerning
lattices is provable in \RCA.
Revised 12/2010. To appear in Archive for Mathematical Logi
Iterative forcing and hyperimmunity in reverse mathematics
The separation between two theorems in reverse mathematics is usually done by
constructing a Turing ideal satisfying a theorem P and avoiding the solutions
to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a
forcing technique for iterating a computable non-reducibility in order to
separate theorems over omega-models. In this paper, we present a modularized
version of their framework in terms of preservation of hyperimmunity and show
that it is powerful enough to obtain the same separations results as Wang did
with his notion of preservation of definitions.Comment: 15 page
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