-cohesive sets

Author:
Barbara F. Ryan

Journal:
Trans. Amer. Math. Soc. **202** (1975), 161-171

MSC:
Primary 02F40

DOI:
https://doi.org/10.1090/S0002-9947-1975-0363848-8

MathSciNet review:
0363848

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Abstract | References | Similar Articles | Additional Information

Abstract: We define and investigate -cohesiveness, a strong notion of indecomposability for subsets of the integers and their isols. This notion says, for example, that if is the isol of an -cohesive set then, for any integer implies that, for some integer or . From this it follows that if , the collection of almost recursive combinatorial polynomials, then the predecessors of are limited to isols where . We show existence of -cohesive sets. And we show that the isol of an -cohesive set is an -order indecomposable isol as defined by Manaster. This gives an alternate proof to one half of Ellentuck's theorem showing a simple algebraic difference between the isols and cosimple isols. In the last section we study functions of several variables when applied to isols of -cohesive sets.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0363848-8

Keywords:
Isols,
-cohesive sets,
almost recursive combinatorial functions,
predecessors of isols,
higher-order indecomposable isols,
universal isols

Article copyright:
© Copyright 1975
American Mathematical Society