## Co-recursively enumerable structures |

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a-eff algebraic structures algebraically closed set algebraically closed subsets assume Boolean algebra Bs+1 category argument codomain combinatorial functors construction Dcpk(n Dedekind Definition dense types Duplication lemma elementary isomorphism exists final value finite algebraically closed finite field finite set function f hence Hs_1 HS,V Ht_1 i e H implies ix(x KS+1 least element Let H Let sQ lim x(i,s morphism Nerode Ng(s Ng(s+l otherwise go partial recursive functions positive requirements priority method productive center contained productive function productive with productive put into H r.e. independent set r.e. sequence r.e. set reaches a final recursion theory recursively enumerable recursively presented model regular sequence Req-closed satisfied by stage sequence n(t sequence of elements set constructions soundly based stable value stage s+1 stage sQ suitable category Theorem theory vector space Vj+1 x e H x(s+l