Mathematical Logic Quarterly 51 (6):570-578 (2005)

Abstract
Given a π -institution I , a hierarchy of π -institutions I is constructed, for n ≥ 1. We call I the n-th order counterpart of I . The second-order counterpart of a deductive π -institution is a Gentzen π -institution, i.e. a π -institution associated with a structural Gentzen system in a canonical way. So, by analogy, the second order counterpart I of I is also called the “Gentzenization” of I . In the main result of the paper, it is shown that I is strongly Gentzen , i.e. it is deductively equivalent to its Gentzenization via a special deductive equivalence, if and only if it has the deduction-detachment property
Keywords category of theories  Leibniz operator  equivalent institutions  Algebraic logic  metalogical properties  algebraizable logics  Gentzen institutions  lattice of theories  algebraizable institutions  equivalent deductive systems  Gentzen systems  deduction‐detachment theorem
Categories (categorize this paper)
DOI 10.1002/malq.200310132
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 55,981
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

A Survey of Abstract Algebraic Logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Equivalential and Algebraizable Logics.Burghard Herrmann - 1996 - Studia Logica 57 (2-3):419 - 436.

View all 18 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Categorical Abstract Algebraic Logic: Models of Π-Institutions.George Voutsadakis - 2005 - Notre Dame Journal of Formal Logic 46 (4):439-460.
Categorical Abstract Algebraic Logic: More on Protoalgebraicity.George Voutsadakis - 2006 - Notre Dame Journal of Formal Logic 47 (4):487-514.
Algebraic Semantics for Deductive Systems.W. J. Blok & J. Rebagliato - 2003 - Studia Logica 74 (1-2):153 - 180.

Analytics

Added to PP index
2013-12-01

Total views
12 ( #750,409 of 2,403,518 )

Recent downloads (6 months)
2 ( #360,890 of 2,403,518 )

How can I increase my downloads?

Downloads

My notes