Consistency and existence by v1.00 last updated: 1 oct 2000 please send your comments to abo
| Abstract | On the one hand, first-order theories are able to assert the existence of objects. For instance, ZF set theory asserts the existence of objects called the power set, while Peano Arithmetic asserts the existence of zero. On the other hand, a first-order theory may or not be consistent: it is if and only if no contradiction is a theorem. Let us ask, What is the connection between consistency and existence? | |||||||||
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Similar books and articlesGeorge Kafkoulis (1994). The Consistency Strength of an Infinitary Ramsey Property. Journal of Symbolic Logic 59 (4):1158-1195.
Harvey Friedman (1977). On the Derivability of Instantiation Properties. Journal of Symbolic Logic 42 (4):506-514.
Enrico Moriconi (2003). On the Meaning of Hilbert's Consistency Problem (Paris, 1900). Synthese 137 (1-2):129 - 139.
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