Vol. 42, No. 3, 1972

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Universal cosimple isols

Erik Maurice Ellentuck

Vol. 42 (1972), No. 3, 629–638

Our results follow from a single priority scheme which we give in detail. They are (i) if an arbitrary n + 1-ary relation over the nonnegative integers determines an n-ary function, then its canonical extension to the isols determines a function on the cosimple isols if and only if the function determined on the integers is an almost recursive combinatorial function, and (ii) every countable partially ordered set can be embedded in (a) the cosimple isols, and even more (b) the cosimple regressive isols. The remaining material generalizes and extends these results.

Mathematical Subject Classification
Primary: 02F40
Received: 27 April 1971
Published: 1 September 1972
Erik Maurice Ellentuck