Drag to reposition

We reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every $\nu \in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik. the iterated forcing $R_{\lambda +1}$ used in this paper has the property that if λ is a cardinal less then κ then $R_{\lambda + 1}$ can be factored in V as $R_{\kappa + 1} = R_{\lambda + 1} \times R_{\lambda + 1, \kappa}$ where $\mid R_{\lambda +1}\mid \leq \lambda^+$ and $R_{\lambda + 1, \kappa}$ does not add any new subsets of λ

A tension between perspectives that emphasize deterministic versus stochastic processes has sparked controversy in ecology since pre-Darwinian times. The most recent manifestation of the contrasting perspectives arose with Hubbell’s proposed “neutral theory”, which hypothesizes a paramount role for stochasticity in ecological community composition. Here we shall refer to the deterministic and the stochastic perspectives as the niche-based and neutral-based research programs, respectively. Our goal is to represent these perspectives in the context of Lakatos’ notion of a scientific research program. We argue that the niche-based program exhibits all the characteristics of a robust, progressive research program, including the ability to deal with disconfirming data by generating new testable predictions within the program. In contrast, the neutral-based program succeeds as a mathematical tool to capture, as epiphenomena, broad-scale patterns of ecological communities but appears to handle disconfirming data by incorporating hypotheses and assumptions from outside the program, specifically, from the niche-based program. We conclude that the neutral research program fits the Lakatosian characterization of a degenerate research program.