A Model of the Arithmetic of Alephs in the Equation Calculus
β Scribed by R. J. Plymen
- Publisher
- John Wiley and Sons
- Year
- 1961
- Tongue
- English
- Weight
- 73 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0044-3050
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π SIMILAR VOLUMES
## Abstract Let __M__ be a model of first order Peano arithmetic (**PA**) and __I__ an initial segment of __M__ that is closed under multiplication. Let__M__~0~ be the {0, 1,+}βreduct of__M__. We show that there is another model __N__ of **PA** that is also an expansion of __M__~0~ such that __a__
## Abstract Since in Heyting Arithmetic (HA) all atomic formulas are decidable, a Kripke model for HA may be regarded classically as a collection of classical structures for the language of arithmetic, partially ordered by the submodel relation. The obvious question is then: are these classical str
PA we define the rfcursively saturated part of XU by RS(9Jl) = ( a E $1: ( 3 8 < YJ?) ( a E )%I and 8 is recursively saturated)). We shall study various possibilities for the relationship between 912 and RS(XU). Tliii paper has grown out of our observation that it may happen that , D is a simple ex