### A New Solution to a Problem of Hosoi and Ono

Michael Zakharyaschev
Source: Notre Dame J. Formal Logic Volume 35, Number 3 (1994), 450-457.

#### Abstract

This paper gives a new, purely semantic proof of the following theorem: if an intermediate propositional logic L has the disjunction property then a disjunction free formula is provable in L iff it is provable in intuitionistic logic. The main idea of the proof is to use the well-known semantic criterion of the disjunction property for "simulating" finite binary trees (which characterize the disjunction free fragment of intuitionistic logic) by general frames.

First Page:
Primary Subjects: 03B55
Secondary Subjects: 03B45
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1040511350
Mathematical Reviews number (MathSciNet): MR1326126
Digital Object Identifier: doi:10.1305/ndjfl/1040511350
Zentralblatt MATH identifier: 0837.03025

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