Unifying the model theory of first-order and second-order arithmetic via WKL0⁎

On the second order first zagreb index

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

First-Order Proof Theory of Arithmetic

From Bounded Arithmetic to Second Order Arithmetic via Automorphisms

In this paper we examine the relationship between automorphisms of models of I∆0 (bounded arithmetic) and strong systems of arithmetic, such as PA, ACA0 (arithmetical comprehension schema with restricted induction), and Z2 (second order arithmetic). For example, we establish the following characterization of PA by proving a “reversal” of a theorem of Gaifman: Theorem. The following are equivale...

Towards unifying second-order theory of likelihoods and pseudolikelihoods

Theory is developed to show that second-order distributional behaviour of pseudolikelihood ratios can be modified to resemble that of likelihood counterparts by means of a suitable adjustment. The latter is conceived to enable the Bartlett correction for pseudolikelihood ratios when inference focuses on a scalar parameter. The proposed methodology can be framed in the likelihood setting where i...

CZF and Second Order Arithmetic

Constructive ZF + full Separation is shown to be equiconsistent with Second Order Arithmetic.