The paper deals with the formalization of the principle of strong mathematical induction: (SMI) If a number has a property whenever all of its predecessors do, then all numbers have that property. According to
principle of induction on the set \(\omega \) of the natural numbers, and the fact that the set \(\omega ^\omega \) of the infinite sequences of natural numbers is closed under the recursion-theoretic operations. the reason that we use a basic theory different in spirit from the basic...
We analyze the classical proof of Paris and Kirby, showing that Σn+1-collection is not provable using Σn-induction. We then mention another principle that is also violated in the model of Paris and Kirby and that might be weaker than Σn+1-collection: there is no Σn+1 definable boun...
Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math. 216(1) (2007) 89-117] and Steel [PFA implies AD(L(R)), J. Symbolic Logic 70(4) (2005) 1255-1296], we show that the failure of square principle at a singular strong limit cardinal implies that ...
Now the From theta dichotomy principle (see [9, Cor. 9.2]) tells us that V ,W (π ∗) is zero as claimed. For the second claim, assume again that (·, ·)π is non-zero. Non-negativity of (·, ·)π follows immediately from Thm A.5 of [17]. One sets the groups G and...
Therefore, the demiclosedness principle (Lemma 2.1) ensures that each weak limit point of is a fixed point of the nonexpansive mapping , that is, a point of the solution set of SFP (1.1). One of the key ingredients of the proof is the following conclusion: (4.18) where is the minimu...
Based on the principle of power conservation, 𝑃𝑑𝑐_𝑚𝑎𝑥Pdc_max is: 𝑃𝑑𝑐=32𝐸𝑚𝑖𝑑−32(𝑅+𝑅𝑆𝐷𝐵𝑅)𝑖2𝑑Pdc=32Emid−32(R+RSDBR)id2 (33) By solving 𝑑𝑃𝑑𝑐/𝑑𝑖𝑑=0dPdc/did=0, it leads to:...