THE POSET OF ALL LOGICS I: INTERPRETATIONS AND LATTICE STRUCTURE

被引：3
作者：
Jansana, R. [1 ]
Moraschini, T. [1 ]
机构：
[1] Univ Barcelona, Dept Philosophy, Carrer Montalegre 6, Barcelona 08001, Spain
来源：
JOURNAL OF SYMBOLIC LOGIC | 2021年 / 86卷 / 03期
关键词：
abstract algebraic logic; Leibniz hierarchy; Maltsev condition; equivalential logic; interpretability; poset of all logics; VARIETIES; SEMILATTICES;
D O I：
10.1017/jsl.2021.48
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A notion of interpretation between arbitrary logics is introduced, and the poset Log of all logics ordered under interpretability is studied. It is shown that in Log infima of arbitrarily large sets exist, but binary suprema in general do not. On the other hand, the existence of suprema of sets of equivalential logics is established. The relations between Log and the lattice of interpretability types of varieties are investigated.
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页码：935 / 964
页数：30
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