منابع مشابه
Information-Theoretic Incompleteness
We propose an improved definition of the complexity of a formal axiomatic system: this is now taken to be the minimum size of a selfdelimiting program for enumerating the set of theorems of the formal system. Using this new definition, we show (a) that no formal system of complexity n can exhibit a specific object with complexity greater than n + c, and (b) that a formal system of complexity n ...
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In this paper we briefly review and analyze three published proofs of Chaitin’s theorem, the celebrated information-theoretic version of Gödel’s incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to all these demonstrations.
متن کاملModel theoretic proofs of the incompleteness theorems
Godel's proofs of the incompleteness theorems are frequently discussed in the context of constructive or nitary viewpoint. Godel showed a concrete independent statement of arithmetic and the proof does not contain any transcendental argument. On the other hand, the completeness theorem asserts that a sentence is not derivable from a theory if and only if there exists a model of the theory whi...
متن کاملIncompleteness in information integration
Information integration is becoming a critical problem for both businesses and individuals. The data, especially the one that comes from the Web, is naturally incomplete, that is, some data values may be unknown or lost because of communication problems, hidden due to privacy considerations. At the same time research in (virtual) integration in the community focusses on null-free sources and ad...
متن کاملInformation Revelation and Market Incompleteness
This paper introduces a theory of market incompleteness based on the information transmission role of prices and its adverse impact on the provision of insurance in financial markets. We analyse a simple security design model in which the number and payoff of securities are endogenous. Agents have rational expectations and differ in information, endowments, and attitudes toward risk. When marke...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 1992
ISSN: 0096-3003
DOI: 10.1016/0096-3003(92)90099-m