Lukasiewicz's Logics And Prime Numbers - Brossura

Karpenko, Alexander S.

Brossura

ISBN 10: 0955117038 ISBN 13: 9780955117039

Casa editrice: Luniver Pr, 2006

Riassunto

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.

Su questa edizione

• Editore: Luniver Pr
• Data di pubblicazione: 2006
• ISBN 10: 0955117038
• ISBN 13: 9780955117039
• Rilegatura: Copertina flessibile
• Numero di pagine: 168