{"product_id":"9780955117039","title":"Lukasiewicz's Logics and Prime Numbers","description":"Is there any link between the doctrine of logical fatalism and prime numbers? What do logic and prime numbers have in common?\u003cbr\u003e 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. \u003cbr\u003e Amazingly, combination of logics of prime numbers led to uncovering a law of generation of classes of prime numbers. \u003cbr\u003e 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.","brand":"Luniver Press","offers":[{"title":"Default Title","offer_id":48049263313136,"sku":"9780955117039","price":25.4,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9780955117039_p0.jpg?v=1763871251","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9780955117039","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}