In:
Journal of Symbolic Logic, Cambridge University Press (CUP), Vol. 23, No. 2 ( 1958-06), p. 149-154
Abstract:
In 1951, Horn obtained a sufficient condition for an arithmetical class to be closed under direct product. A natural question which arose was whether Horn's condition is also necessary. We obtain a negative answer to that question. We shall discuss relational systems of the form where A and R are non-empty sets; each element of R is an ordered triple 〈 a, b, c 〉, with a, b, c ∈ A . 1 If the triple 〈 a, b, c 〉 belongs to the relation R , we write R ( a, b, c ); if 〈 a, b, c 〉 ∉ R , we write ( a, b, c ). If x 0 , x 1 and x 2 are variables, then R ( x 0 , x 1 , x 2 ) and x 0 = x 1 are predicates . The expressions ( x 0 , x 1 , x 2 ) and x 0 ≠ x 1 will be referred to as negations of predicates . We speak of α 1 , …, α n as terms of the disjunction α 1 ∨ … ∨ α n and as factors of the conjunction α 1 ∧ … ∧ α n . A sentence (open, closed or neither) of the form where each Q i (if there be any) is either the universal or the existential quantifier and each α i, l is either a predicate or a negation of a predicate, is said to be in prenex disjunctive normal form .
Type of Medium:
Online Resource
ISSN:
0022-4812
,
1943-5886
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1958
detail.hit.zdb_id:
2010607-5
SSG:
5,1
SSG:
17,1
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