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.
Citation
Michael Zakharyaschev. "A New Solution to a Problem of Hosoi and Ono." Notre Dame J. Formal Logic 35 (3) 450 - 457, /Summer 1994. https://doi.org/10.1305/ndjfl/1040511350
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