Every theory we will consider will be in a language that has a name ṅ for each n ∈ ω. For example, the name for 2 ∈ ω in the language LΩ of arithmetic is the term “1 + 1”. The results stated will only apply to countable languages. This requirement is implicit in the hypothesis of the existence of an enumeration of all formulas with one free variable, for example. We also assume that formulas an...

In this paper, we introduce a new fragment of the rst-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator (Since or Until) have at most one free variable. We show that the satissability problem for monodic formulas in various linear time structures can be reduced to the satissability problem for a certain fragment of classical rst-order...

where μ = IE(X) ∈ IR and σ = var(X) > 0 are the mean and variance of X . We write X ∼ N (μ, σ). Note that X = σZ + μ for Z ∼ N (0, 1) (called standard Gaussian) and where the equality holds in distribution. Clearly, this distribution has unbounded support but it is well known that it has almost bounded support in the following sense: IP(|X −μ| ≤ 3σ) ≃ 0.997. This is due to the fast decay of the...

Prey that do not escape when attacked by lethal predators die. Even prey that suffer nonlethal injuries inflicted by predators may incur substantial costs, such as reduced ability to reproduce, reduced social status, reduced ability to forage, and reduced ability to escape in later encounters with predators. Unsuccessful escape reduces fitness. A prey that is killed by a predator loses all fitn...

Econometric analyses of treatment response often use instrumental variable (IV) assumptions to identify treatment effects. The traditional IV assumption holds that mean response is constant across the subpopulations of persons with different values of an observed covariate. Manski and Pepper (2000) introduced monotone instrumental variable (MIV) assumptions, which replace equalities with weak i...