Lukasiewicz's Logics and Prime Numbers（进口原版，国内现货）
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作者Alexander S Karpenko (Author)
出版社Luniver Press
ISBN9780955117039
出版时间2006
装帧平装
页数168页
货号a5
上书时间2020-06-04
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Is there any link between the doctrine of logical fatalism and prime numbers? What do logic and prime numbers have in common? The book adopts truth functional approach to examine functional properties of finite valued Łukasiewicz logics Łn+1. Prime numbers are defined in algebraic-logical terms (Finn's theorem) and represented as rooted trees. The author designs an algorithm which for every prime number n constructs a rooted tree where nodes are natural numbers and n is a root. Finite valued logics Kn+1 are specified that they have tautologies if and only if n is a prime number. It is discovered that Kn+1 have the same functional properties as Łn+1 whenever n is a prime number. Thus, Kn+1 are 'logics' of prime numbers. Amazingly, combination of logics of prime numbers led to uncovering a law of generation of classes of prime numbers. Along with characterization of prime numbers author also gives characterization, in terms of Łukasiewicz logical matrices, of powers of primes, odd numbers, and even numbers.
Alexander S. Karpenko, D.Sci. (1991), PhD (1979), is Head of Department of Logic, Institute of Philosophy, Russian Academy of Sciences, and Professor of Moscow State University.
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