Congruence relations, filters, ideals, and definability in lattices of α-recursively enumerable sets

Publisher： Cambridge University Press

E-ISSN： 1943-5886|41|2|405-418

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.41, Iss.2, 1976-06, pp. : 405-418

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Abstract

Throughout this paper, α will denote an admissible ordinal. Let (α) denote the lattice of α-r.e. sets, i.e., the lattice whose elements are the α-r.e. sets, and whose ordering is given by set inclusion. Call a set A ∈ (α)α*-finite if it is α-finite and has ordertype < α* (the Σ1-projectum of α). The α*-finite sets form an ideal of (α), and factoring (α) by this ideal, we obtain the quotient lattice *(α).

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