✦ LIBER ✦

A simplification of a completeness proof of Guaspari and Solovay

✍ Scribed by Dick H. J. Jongh

Book ID: 104744872
Publisher: Springer Netherlands
Year: 1987
Tongue: English
Weight: 401 KB
Volume: 46
Category: Article
ISSN: 0039-3215
DOI: 10.1007/bf00370380

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✦ Synopsis

The modM completeness proofs of Guasp~ri and Solovay (1979) for their systems R and R-are improved and the relationship between R and R-is clarified. Guaspari-Sclovay (1979) a modal completeness proof was given for a system R which extends the provabflity logic L by the incorporation of the symbols -~ and <: for witness comparisons. These symbols co,n be put between two boxed formulae A and B (i.e. formulae of the form []C) to obtain A -~ B and A ~ B. This enables one to study Rosser sentences in a propositional context. The methods used by GusJspari and Solovay for their completeness proof were somewhat cumbersome. In the extensive survey of the whole subject, Smorynski (1985), somewhat smoother and more complete presentation is given; here we will give still simpler proofs in such a way that the relationship with other systems like the ones ef de gongh-Montagna (1987) is clarified and an ~mMgam~tion of 9 these Systems can be attempted: