A family of maximal subalgebras of R. Robinson's algebra

A. N. Degtev

Tyumen State University

Abstract: All maximal sub algebras of the algebra of primitive recursive functions $\langle\Phi;+,*,i\rangle$, whose basic sets contain the set
$$ A+\{f:f\equiv0\vee(\forall\,x)(x>0\Rightarrow f(x)>0)\} $$
are described. It is shown that they are continuum in number.

UDC: 517.1

Received: 17.12.1975

 English version: Mathematical Notes, 1977, 22:4, 775–778

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