-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